Cherniha Roman
Publications
Books, Papers and Citation
• Approximately 120 scientific papers and 4 books are published up to date the 1st Jan, 2021 ( thesis of conferences and preprints are not taken into account).
• According to the WEB of Science (Core collection) data base, 68 papers among them were indexed, which were cited 807 times and the Hirsch index is h=18 (up to date Jan 1, 2022).
•According to the Scopus data base 78 papers were indexed, which were cited 980 times and the Hirsch index is h=20 (up to date Jan 1, 2022).
• The most cited papers are [5], [9] and [15].
Books
Roman Cherniha and Vasyl’ Davydovych. Nonlinear reaction-diffusion systems -- conditional symmetry, exact solutions and their applications in biology. -- Lecture Notes in Mathematics. Vol. 2196 .Springer , 2017.
R. Cherniha, M. Serov, O. Pliukhin. Nonlinear reaction-diffusion-convection equations: Lie and conditional symmetry, exact solutions and their applications. CRC Press (USA), 2018.
R.M. Cherniha Equations of Mathematical Physics. Kyiv: Publishing house 'Kyiv-Mohyla Academy', 2012 (textbook in Ukrainian, summary in English) ISBN 978-966-2410-14-3
`Lie and Non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models.' Edited by Roman M. Cherniha. MDPI, Basel, 2017.
Papers published in major international journals with impact-factor
(Web of Science http://thomsonreuters.com/web-of-science/ )
1 Fushchych W.I and Cherniha R.M The Galilean relativistic principle and nonlinear partial differential equations. J.Phys.A.:Math. and Gen.--1985.-v.18, N 18.--P.3491―3503.
2 Cherniha R. and Cherniha N. Exact solution of a class of nonlinear boundary value problems with moving boundaries. J.Phys.A.:Math. and Gen. 1993.-v.26, N 18.--P. L935-940.
3 Fushchych W.I and Cherniha R.M. Galilei-invariant systems of nonlinear systems of evolution equations. J.Phys.A: Math.Gen. -1995. -vol. 28, P.5569-5579.
4 Cherniha R. A constructive method for obtaining new exact solutions of nonlinear evolution equations. Rept. Math. Phys.-1996.- vol. 38, P.301-312.
5 Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms. European J. of Appl. Math.--1998. - vol. 9, No 5, P.527-542.
6 Cherniha R. New Non-Lie Ansaetze and Exact Solutions of Nonlinear Reaction-Diffusion-Convection Equations. J. Phys. A: Math.Gen. -- 1998.-vol. 31, No 40, P.8179-8198.
7 Cherniha R. and Fehribach J. New exact solutions for a free boundary system. J.Phys. A: Math. and Gen. ― 1998. -- vol. 31, No 16, P.3815-3829.
8 Cherniha R. New Exact Solutions of Nonlinear Reaction-Diffusion Equations. Rept. Math. Phys. ―1998.―V.41, No 2, P. 333-349.
9 Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen. -- 2000.-- V.33, No 2-- P.267-282.
10 Cherniha R. and King J. R. Addendum. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen.-- 2000.-- V.33, No 43-- P.7839-41.
11 Cherniha R. Lie Symmetries of Nonlinear Two-dimensional Reaction-Diffusion Systems. Rept. Math. Phys.--2000. ―v.46. ―P. 63-76.
12 Cherniha R. and Dutka V. Exact and Numerical Solutions of the Generalized Fisher Equation. Rept. Math. Phys.--2001.-v.47.--P. 393-411.
13 Cherniha R. M. Nonlinear Galilei-invariant PDEs with infinite-dimensional Lie symmetry. J.Math.Anal.Appl.--2001.-v.253.-- P.126-141.
14 Cherniha R and Serov M. Nonlinear Systems of the Burgers-type Equations: Lie and Q-condi-tional Symmetries, Ansaetze and Solutions. J.Math. Anal. Appl.--2003.-v.282.--P.305-328.
15 Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems. II. J. Phys. A: Math. and Gen.--- 2003.-- vol.36. -- P.~405―425.
16 Cherniha R. and Henkel M On nonlinear partial differential equations with an infinite-dimensional conditional symmetry. J.Math.Anal.Appl.--2004.-v.298.-- P.487--500.
17 Cherniha R. and King J. R. Nonlinear Reaction-Diffusion Systems with Variable Diffusivities: Lie Symmetries, Ansaetze and Exact Solution. J.Math.Anal.Appl.--2005.-v.308.-- P.11--35.
18 Cherniha R. and King J. R. Lie Symmetries and Conservation Laws of Nonlinear Multidimensional Reaction-Diffusion Systems with Variable Diffusivities. IMA J. Appl. Math. 2006 -vol.71 – P.391-408.
19 Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms, II. European J. of Appl. Math. –2006.-v.17.―597-605.
20 R. Cherniha, V.Dutka, J.Stachowska-Pietka and J.Waniewski. Fluid transport in peritoneal dialysis: a mathematical model and numerical solutions. In:Mathematical Modeling of Biological Systems, Vîl..I. Ed. by A.Deutsch et al., Birkhaeuser, P.291-298, 2007
21 Cherniha R. New Q-conditional symmetries end exact solutions reaction-diffusion-convection eduations arising in mathematical biology. J.Math.Anal.Appl. .--2007.-v.326.-- P.783―799.
22 Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of nonlinear -reaction-diffusion-convection equations. J. Phys. A: Math. and Theor.--- 2007.-- vol.40. -- P.~10049―10070.
23 Cherniha R., Serov M. and Rassokha I. Lie Symmetries and Form-preserving Transformations of Reaction-Diffusion-Convection Equations. J.Math.Anal.Appl. .--2008.-v.342.-- P.1363―1379.
24 Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of reaction-diffusion systems with power diffusivities. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 185208 (14pp).
25 Cherniha R. and Myroniuk L. New exact solutions of a nonlinear cross-diffusion system. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 395204 (15pp).
26 Cherniha R. and Kovalenko S. Exact solutions of nonlinear boundary value problems of the Stefan type. J. Phys. A: Math. and Theor.--- 2009.-- vol.42, 355202 (14pp).
27 Cherniha R. and Henkel M The exotic conformal Galilei algebra and nonlinear partial differential equations. J.Math.Anal.Appl.--2010.-v.369.-- P.120--132.
28 Cherniha R. Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems. J. Phys. A: Math. and Theor.--- 2010.-- vol.43, 405207 (13pp).
29 Cherniha R. and Kovalenko S. Lie symmetries and reductions of multidimensional boundary value problems of the Stefan type. J. Phys. A : Math. Theor. --2011.--Vol. 44.,485202 (25 pp).
30 Cherniha R. and Davydovych V. Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system. Math. Comp. Model.—2011.—vol.54, 1238—1251.
31 Cherniha R. and Kovalenko S. Lie symmetries of nonlinear boundary value problems. Commun. Nonlinear Sci. Numer. Simul.--2012.--Vol. 17. P. 71—84.
32 Cherniha R. and Davydovych V. Conditional symmetries and exact solutions of nonlinear reaction–diffusion systems with non-constant diffusivities. Commun. Nonlinear Sci. Numer. Simul.--2012.--Vol. 17. P. 3177—88.
33 Cherniha R. and Davydovych V. Lie and conditional symmetries of the three-component diffusive Lotka-Volterra system. J. Phys. A: Math. and Theor.--- 2013.-- vol.46, 185204 (14pp).
34 Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of reaction-diffusion-convection equations with exponential nonlinearities. J.Math.Anal.Appl.--2013.-vol.403.-- P.23--37.
35 Cherniha R. and Didovych M. Exact solutions of the simplified Keller-Segel model. Commun. Nonlinear Sci. Numer. Simul.--2013.--Vol. 18. P. 2960-297.
36 Cherniha R. Conditional symmetries for boundary value problems: new definition and its application for nonlinear problems. Miskolc Math. Notes --2013.--Vol. 14. P. 637-646.
37 R. Cherniha, J. Stachowska-Pietka and J. Waniewski. A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis. Int. J. Appl. Math. Comp. Sci., 2014, vol.24, P.837-851.
38 . Cherniha R and Davydovych V Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations in: Algebra, Geomerty and Mathematical Physics, Springer Proc. in Mathematics & Statistics, 2014, vol.85, 533—553.
39 Cherniha R and Davydovych V Nonlinear reaction–diffusion systems with a non-constant diffusivity: Conditional symmetries in no-go case. Appl. Math. C omput. 2015, vol. 268. – P. 23–34.
40 Cherniha R. and King JR Lie and Conditional Symmetries of a Class of Nonlinear (1+2)-dimensional Boundary Value Problems. Symmetry. 2015, vol. 7. P. 1410–1435.
41 Cherniha R., King JR and Kovalenko S. Lie symmetry properties of nonlinear
reaction-diffusion equations with gradient-dependent diffusivity.
Commun. Nonlinear Sci. Numer. Simul.--2016.--Vol. 36. P.98—108.
42 R. Cherniha, K. Gozak and J. Waniewski.Exact and numerical solutions of a spatially-distributed mathematical model for fluid and solute transport in peritoneal dialysis. Symmetry --2016. –Vol. 8 (6). 50. doi:10.3390/sym8060050
43 Cherniha R. and Didovych M. A (1 + 2)-Dimensional Simplified Keller–Segel Model:
Lie Symmetry and Exact Solutions. II Symmetry –2017—Vol. 9, 13; doi:10.3390/sym9010013
44 Cherniha R., Davydovych V. and Muzyka. Lie symmetries of the Shigesada–Kawasaki–Teramoto system. Commun Nonlinear Sci Numer Simulat. 2017.-- Vol.45. P.81-92.
45 R. Cherniha, V. Davydovych and JR King. Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model. Symmetry 2018, 10, 171; doi:10.3390/sym10050171
46 R. Cherniha, M.Serov, and O. Pliukhin. Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions -- Symmetry 2018, 10, 123; doi:10.3390/sym10040123
47 R. Cherniha and V. Davydovych. A hunter-gatherer--farmer population model: Lie
symmetries, exact solutions and their interpretation. Euro. J. of Applied Mathematics ,2019, vol. 30, pp. 338–357 doi:10.1017/S0956792518000104
48 Cherniha, R., Davydovych, V.Lie symmetries, reduction and exact solutions of the (1+2)-dimensional nonlinear problem modeling the solid tumour growth. Commun Nonlinear Sci Numer Simulat. 2020. Vol.80, 104980 https://doi.org/10.1016/j.cnsns.2019.104980
49 R . Cherniha. Comments on the paper «Lie symmetry analysis, explicit solutions, and conservation laws of a spatially two-dimensional burgers-huxley equation.» Symmetry, 2020, 12(6), 900. https://doi.org/10.3390/sym12060900
50 Cherniha, R.; Davydovych, V. A Mathematical Model for the COVID-19 Outbreak and Its Applications. Symmetry 2020, 12, 990. https://doi.org/10.3390/sym12060990
51 Cherniha, R.; Davydovych, V. Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers. Entropy 2020, 22, 154. https://doi.org/10.3390/e22020154
52 Cherniha, R.; Stachowska-Pietka, J.; Waniewski, J. A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples. Symmetry 2020, 12, 396. https://doi.org/10.3390/sym12030396
53 Cherniha, R.; Davydovych, V. Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model. Euro. J. of Applied Mathematics ,2020. https://doi.org/10.1017/S0956792520000121
54 R.Cherniha, M.Serov,Y.Prystavka, A complete Lie symmetry classification of a class of (1+2)-dimensional reaction-diffusion-convection equation, CNSNS 92 (2021), 105466 https://doi.org/10.1016/j.cnsns.2020.105466
55 R.Cherniha, Comments on the paper ``Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry approach'' CNSNS 102 (2021), 105922 https://doi.org/10.1016/j.cnsns.2021.105922
56 Cherniha R., Davydovych V., Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model, Euro. J. Appl. Math. 32 (2021), 280–300.https://doi.org/10.1017/S0956792520000121
57 Cherniha R., Davydovych V., New conditional symmetries and exact solutions of the diffusive two-component Lotka–Volterra system, Mathematics 9 (2021), no. 16, 1984, 17 pp.https://doi.org/10.3390/math9161984
58 Davydovych V.V., Cherniha R.M., On a nonlinear mathematical model for the description of the competition and coexistence of different-language speakers, J. Math. Sci. 256 (2021), 628–639. https://doi.org/10.1007/s10958-021-05449-5
Main publications (in English) published in other scientific journals
A1. Fushchich W. and Cherniga R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions I. Ukrainian Math.J. -1989.- vol.41, P. 1161-67 .
.A2. Fushchich W. and Cherniga R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions II. Ukrainian Math.J. -1989.- vol.41, P.1456-63.
A3. Cherniga R.M. and Odnorozhenko I.G. Studies of the processes of melting and evaporation of metals under the action of laser radiation pulses. Promyshlennaya Teplotekhnika-1991-vol.13- No-4, P.51-59 (English translation in: Heat Transfer Research, USA).
A4. Cherniha R. Galilei-invariant non-linear PDEs and their exact solutions. J. Nonlinear Math. Phys. --1995.- vol. 2- No 3-4, p.374-383.
A5. Fushchych W.I., Cherniha R. and Chopyk V. On unique symmetry of two nonlinear generalizations of the Schroedinger equation. J. Nonlinear Math. Phys. -1996.-vol.3, N 3-4, P.296-301.
A6. Cherniha R. and Wilhelmsson H. Symmetry and exact solution of heat-mass transfer equations in thermonuclear plasma. Ukrainian Math. J. 1996.- vol. 48-- No 9, P.1434--1449
A7. Cherniha R. New spherycally symmetryc solutions of nonlinear Schroedinger equations. J. Nonlin. Math. Phys.-1997.- Vol.4, No.1-2.P.107--113.
A8. Cherniha R. Application of a constructive method for obtaining non-Lie solutions of nonlinear evolution equations. Ukrainian Math. J. - 1997.- vol. 49-- No 6, P.910--924
A9. Cherniha R. New Exact Solutions of a Nonlinear Reaction-Diffusion Equation Arising in Mathematical Biology and Their Properties. Ukrainian Math. J. 2001.- vol.53-- No 10, P.1712--1727.
A10. Cherniha R. and Dutka V. A. A diffusive Lotka-Volterra system: Lie symmetries, exact and numerical solutions. Ukrainian Math. J. 2004.- vol.56-- No 10, P.1665—1675.
A11. Cherniha R. and Waniewski J. Exact solutions of a mathematical model for fluid transport in peritoneal dialysis. Ukrainian Math. J. – 2005.- vol. 57. P.1112--1119.
A12. J.Waniewski, V.Dutka, J.Stachowska-Pietka, R. Cherniha. Distributed Modeling of Glucose-Induced Osmotic Flow. Advances in Peritoneal Dialysis―2007―vol.23 (part 1)―P.2―6.
A13. Cherniha R. and Pliukhin O. Symmetries and solutions of reaction-diffusion-convection equations with power diffusivities. PAMM Proc. Math.Mech.-- 2007-vol.7, P.2040065-6.
A14. Cherniha R. and Myroniuk L. Lie Symmetries and Exact Solutions of a Class of Thin Film Equations. Journal of Physical Mathematics – 2010-- Vol: 2 P. 1-19.
A15. Cherniha R. and Kovalenko S. Lie symmetry of a class of nonlinear boundary value
problems with free boundaries. Banach Center Publ. --2011. --Vol. 93. P. 95—104
A16. Cherniha R. and Pliukhin O. Nonlinear evolution equations with exponential
nonlinearities: conditional symmetries and exact solutions. Banach Center Publ. --2011. --Vol. 93. P. 105—115.
À17 J Waniewski, J Stachowska-Pietka, R Cherniha, B Lindholm DOES THE PERITONEUM SWELLS OR SHRINK DURING PERITONEAL DIALYSIS?
Nephrology Dialysis Transplantation (Oxford University Press)—2020--vol. 35, Supplement_3, gfaa142. P1158
A18 J Waniewski, J Stachowska-Pietka, R Cherniha, B Lindholm. SWELLING OF PERITONEAL TISSUE DURING PERITONEAL DIALYSIS: COMPUTATIONAL ASSESSMENT USING POROELASTIC THEORY. Nephrology Dialysis Transplantation (Oxford University Press)— 2020--vol. 36, Supplement_1, gfab101. 0016.
Last time updated: 10th January, 2022
• Approximately 120 scientific papers and 4 books are published up to date the 1st Jan, 2021 ( thesis of conferences and preprints are not taken into account).
• According to the WEB of Science (Core collection) data base, 68 papers among them were indexed, which were cited 807 times and the Hirsch index is h=18 (up to date Jan 1, 2022).
•According to the Scopus data base 78 papers were indexed, which were cited 980 times and the Hirsch index is h=20 (up to date Jan 1, 2022).
• The most cited papers are [5], [9] and [15].
Books
Roman Cherniha and Vasyl’ Davydovych. Nonlinear reaction-diffusion systems -- conditional symmetry, exact solutions and their applications in biology. -- Lecture Notes in Mathematics. Vol. 2196 .Springer , 2017.
R. Cherniha, M. Serov, O. Pliukhin. Nonlinear reaction-diffusion-convection equations: Lie and conditional symmetry, exact solutions and their applications. CRC Press (USA), 2018.
R.M. Cherniha Equations of Mathematical Physics. Kyiv: Publishing house 'Kyiv-Mohyla Academy', 2012 (textbook in Ukrainian, summary in English) ISBN 978-966-2410-14-3
`Lie and Non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models.' Edited by Roman M. Cherniha. MDPI, Basel, 2017.
Papers published in major international journals with impact-factor
(Web of Science http://thomsonreuters.com/web-of-science/ )
1 Fushchych W.I and Cherniha R.M The Galilean relativistic principle and nonlinear partial differential equations. J.Phys.A.:Math. and Gen.--1985.-v.18, N 18.--P.3491―3503.
2 Cherniha R. and Cherniha N. Exact solution of a class of nonlinear boundary value problems with moving boundaries. J.Phys.A.:Math. and Gen. 1993.-v.26, N 18.--P. L935-940.
3 Fushchych W.I and Cherniha R.M. Galilei-invariant systems of nonlinear systems of evolution equations. J.Phys.A: Math.Gen. -1995. -vol. 28, P.5569-5579.
4 Cherniha R. A constructive method for obtaining new exact solutions of nonlinear evolution equations. Rept. Math. Phys.-1996.- vol. 38, P.301-312.
5 Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms. European J. of Appl. Math.--1998. - vol. 9, No 5, P.527-542.
6 Cherniha R. New Non-Lie Ansaetze and Exact Solutions of Nonlinear Reaction-Diffusion-Convection Equations. J. Phys. A: Math.Gen. -- 1998.-vol. 31, No 40, P.8179-8198.
7 Cherniha R. and Fehribach J. New exact solutions for a free boundary system. J.Phys. A: Math. and Gen. ― 1998. -- vol. 31, No 16, P.3815-3829.
8 Cherniha R. New Exact Solutions of Nonlinear Reaction-Diffusion Equations. Rept. Math. Phys. ―1998.―V.41, No 2, P. 333-349.
9 Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen. -- 2000.-- V.33, No 2-- P.267-282.
10 Cherniha R. and King J. R. Addendum. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen.-- 2000.-- V.33, No 43-- P.7839-41.
11 Cherniha R. Lie Symmetries of Nonlinear Two-dimensional Reaction-Diffusion Systems. Rept. Math. Phys.--2000. ―v.46. ―P. 63-76.
12 Cherniha R. and Dutka V. Exact and Numerical Solutions of the Generalized Fisher Equation. Rept. Math. Phys.--2001.-v.47.--P. 393-411.
13 Cherniha R. M. Nonlinear Galilei-invariant PDEs with infinite-dimensional Lie symmetry. J.Math.Anal.Appl.--2001.-v.253.-- P.126-141.
14 Cherniha R and Serov M. Nonlinear Systems of the Burgers-type Equations: Lie and Q-condi-tional Symmetries, Ansaetze and Solutions. J.Math. Anal. Appl.--2003.-v.282.--P.305-328.
15 Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems. II. J. Phys. A: Math. and Gen.--- 2003.-- vol.36. -- P.~405―425.
16 Cherniha R. and Henkel M On nonlinear partial differential equations with an infinite-dimensional conditional symmetry. J.Math.Anal.Appl.--2004.-v.298.-- P.487--500.
17 Cherniha R. and King J. R. Nonlinear Reaction-Diffusion Systems with Variable Diffusivities: Lie Symmetries, Ansaetze and Exact Solution. J.Math.Anal.Appl.--2005.-v.308.-- P.11--35.
18 Cherniha R. and King J. R. Lie Symmetries and Conservation Laws of Nonlinear Multidimensional Reaction-Diffusion Systems with Variable Diffusivities. IMA J. Appl. Math. 2006 -vol.71 – P.391-408.
19 Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms, II. European J. of Appl. Math. –2006.-v.17.―597-605.
20 R. Cherniha, V.Dutka, J.Stachowska-Pietka and J.Waniewski. Fluid transport in peritoneal dialysis: a mathematical model and numerical solutions. In:Mathematical Modeling of Biological Systems, Vîl..I. Ed. by A.Deutsch et al., Birkhaeuser, P.291-298, 2007
21 Cherniha R. New Q-conditional symmetries end exact solutions reaction-diffusion-convection eduations arising in mathematical biology. J.Math.Anal.Appl. .--2007.-v.326.-- P.783―799.
22 Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of nonlinear -reaction-diffusion-convection equations. J. Phys. A: Math. and Theor.--- 2007.-- vol.40. -- P.~10049―10070.
23 Cherniha R., Serov M. and Rassokha I. Lie Symmetries and Form-preserving Transformations of Reaction-Diffusion-Convection Equations. J.Math.Anal.Appl. .--2008.-v.342.-- P.1363―1379.
24 Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of reaction-diffusion systems with power diffusivities. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 185208 (14pp).
25 Cherniha R. and Myroniuk L. New exact solutions of a nonlinear cross-diffusion system. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 395204 (15pp).
26 Cherniha R. and Kovalenko S. Exact solutions of nonlinear boundary value problems of the Stefan type. J. Phys. A: Math. and Theor.--- 2009.-- vol.42, 355202 (14pp).
27 Cherniha R. and Henkel M The exotic conformal Galilei algebra and nonlinear partial differential equations. J.Math.Anal.Appl.--2010.-v.369.-- P.120--132.
28 Cherniha R. Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems. J. Phys. A: Math. and Theor.--- 2010.-- vol.43, 405207 (13pp).
29 Cherniha R. and Kovalenko S. Lie symmetries and reductions of multidimensional boundary value problems of the Stefan type. J. Phys. A : Math. Theor. --2011.--Vol. 44.,485202 (25 pp).
30 Cherniha R. and Davydovych V. Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system. Math. Comp. Model.—2011.—vol.54, 1238—1251.
31 Cherniha R. and Kovalenko S. Lie symmetries of nonlinear boundary value problems. Commun. Nonlinear Sci. Numer. Simul.--2012.--Vol. 17. P. 71—84.
32 Cherniha R. and Davydovych V. Conditional symmetries and exact solutions of nonlinear reaction–diffusion systems with non-constant diffusivities. Commun. Nonlinear Sci. Numer. Simul.--2012.--Vol. 17. P. 3177—88.
33 Cherniha R. and Davydovych V. Lie and conditional symmetries of the three-component diffusive Lotka-Volterra system. J. Phys. A: Math. and Theor.--- 2013.-- vol.46, 185204 (14pp).
34 Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of reaction-diffusion-convection equations with exponential nonlinearities. J.Math.Anal.Appl.--2013.-vol.403.-- P.23--37.
35 Cherniha R. and Didovych M. Exact solutions of the simplified Keller-Segel model. Commun. Nonlinear Sci. Numer. Simul.--2013.--Vol. 18. P. 2960-297.
36 Cherniha R. Conditional symmetries for boundary value problems: new definition and its application for nonlinear problems. Miskolc Math. Notes --2013.--Vol. 14. P. 637-646.
37 R. Cherniha, J. Stachowska-Pietka and J. Waniewski. A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis. Int. J. Appl. Math. Comp. Sci., 2014, vol.24, P.837-851.
38 . Cherniha R and Davydovych V Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations in: Algebra, Geomerty and Mathematical Physics, Springer Proc. in Mathematics & Statistics, 2014, vol.85, 533—553.
39 Cherniha R and Davydovych V Nonlinear reaction–diffusion systems with a non-constant diffusivity: Conditional symmetries in no-go case. Appl. Math. C omput. 2015, vol. 268. – P. 23–34.
40 Cherniha R. and King JR Lie and Conditional Symmetries of a Class of Nonlinear (1+2)-dimensional Boundary Value Problems. Symmetry. 2015, vol. 7. P. 1410–1435.
41 Cherniha R., King JR and Kovalenko S. Lie symmetry properties of nonlinear
reaction-diffusion equations with gradient-dependent diffusivity.
Commun. Nonlinear Sci. Numer. Simul.--2016.--Vol. 36. P.98—108.
42 R. Cherniha, K. Gozak and J. Waniewski.Exact and numerical solutions of a spatially-distributed mathematical model for fluid and solute transport in peritoneal dialysis. Symmetry --2016. –Vol. 8 (6). 50. doi:10.3390/sym8060050
43 Cherniha R. and Didovych M. A (1 + 2)-Dimensional Simplified Keller–Segel Model:
Lie Symmetry and Exact Solutions. II Symmetry –2017—Vol. 9, 13; doi:10.3390/sym9010013
44 Cherniha R., Davydovych V. and Muzyka. Lie symmetries of the Shigesada–Kawasaki–Teramoto system. Commun Nonlinear Sci Numer Simulat. 2017.-- Vol.45. P.81-92.
45 R. Cherniha, V. Davydovych and JR King. Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model. Symmetry 2018, 10, 171; doi:10.3390/sym10050171
46 R. Cherniha, M.Serov, and O. Pliukhin. Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions -- Symmetry 2018, 10, 123; doi:10.3390/sym10040123
47 R. Cherniha and V. Davydovych. A hunter-gatherer--farmer population model: Lie
symmetries, exact solutions and their interpretation. Euro. J. of Applied Mathematics ,2019, vol. 30, pp. 338–357 doi:10.1017/S0956792518000104
48 Cherniha, R., Davydovych, V.Lie symmetries, reduction and exact solutions of the (1+2)-dimensional nonlinear problem modeling the solid tumour growth. Commun Nonlinear Sci Numer Simulat. 2020. Vol.80, 104980 https://doi.org/10.1016/j.cnsns.2019.104980
49 R . Cherniha. Comments on the paper «Lie symmetry analysis, explicit solutions, and conservation laws of a spatially two-dimensional burgers-huxley equation.» Symmetry, 2020, 12(6), 900. https://doi.org/10.3390/sym12060900
50 Cherniha, R.; Davydovych, V. A Mathematical Model for the COVID-19 Outbreak and Its Applications. Symmetry 2020, 12, 990. https://doi.org/10.3390/sym12060990
51 Cherniha, R.; Davydovych, V. Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers. Entropy 2020, 22, 154. https://doi.org/10.3390/e22020154
52 Cherniha, R.; Stachowska-Pietka, J.; Waniewski, J. A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples. Symmetry 2020, 12, 396. https://doi.org/10.3390/sym12030396
53 Cherniha, R.; Davydovych, V. Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model. Euro. J. of Applied Mathematics ,2020. https://doi.org/10.1017/S0956792520000121
54 R.Cherniha, M.Serov,Y.Prystavka, A complete Lie symmetry classification of a class of (1+2)-dimensional reaction-diffusion-convection equation, CNSNS 92 (2021), 105466 https://doi.org/10.1016/j.cnsns.2020.105466
55 R.Cherniha, Comments on the paper ``Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry approach'' CNSNS 102 (2021), 105922 https://doi.org/10.1016/j.cnsns.2021.105922
56 Cherniha R., Davydovych V., Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model, Euro. J. Appl. Math. 32 (2021), 280–300.https://doi.org/10.1017/S0956792520000121
57 Cherniha R., Davydovych V., New conditional symmetries and exact solutions of the diffusive two-component Lotka–Volterra system, Mathematics 9 (2021), no. 16, 1984, 17 pp.https://doi.org/10.3390/math9161984
58 Davydovych V.V., Cherniha R.M., On a nonlinear mathematical model for the description of the competition and coexistence of different-language speakers, J. Math. Sci. 256 (2021), 628–639. https://doi.org/10.1007/s10958-021-05449-5
Main publications (in English) published in other scientific journals
A1. Fushchich W. and Cherniga R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions I. Ukrainian Math.J. -1989.- vol.41, P. 1161-67 .
.A2. Fushchich W. and Cherniga R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions II. Ukrainian Math.J. -1989.- vol.41, P.1456-63.
A3. Cherniga R.M. and Odnorozhenko I.G. Studies of the processes of melting and evaporation of metals under the action of laser radiation pulses. Promyshlennaya Teplotekhnika-1991-vol.13- No-4, P.51-59 (English translation in: Heat Transfer Research, USA).
A4. Cherniha R. Galilei-invariant non-linear PDEs and their exact solutions. J. Nonlinear Math. Phys. --1995.- vol. 2- No 3-4, p.374-383.
A5. Fushchych W.I., Cherniha R. and Chopyk V. On unique symmetry of two nonlinear generalizations of the Schroedinger equation. J. Nonlinear Math. Phys. -1996.-vol.3, N 3-4, P.296-301.
A6. Cherniha R. and Wilhelmsson H. Symmetry and exact solution of heat-mass transfer equations in thermonuclear plasma. Ukrainian Math. J. 1996.- vol. 48-- No 9, P.1434--1449
A7. Cherniha R. New spherycally symmetryc solutions of nonlinear Schroedinger equations. J. Nonlin. Math. Phys.-1997.- Vol.4, No.1-2.P.107--113.
A8. Cherniha R. Application of a constructive method for obtaining non-Lie solutions of nonlinear evolution equations. Ukrainian Math. J. - 1997.- vol. 49-- No 6, P.910--924
A9. Cherniha R. New Exact Solutions of a Nonlinear Reaction-Diffusion Equation Arising in Mathematical Biology and Their Properties. Ukrainian Math. J. 2001.- vol.53-- No 10, P.1712--1727.
A10. Cherniha R. and Dutka V. A. A diffusive Lotka-Volterra system: Lie symmetries, exact and numerical solutions. Ukrainian Math. J. 2004.- vol.56-- No 10, P.1665—1675.
A11. Cherniha R. and Waniewski J. Exact solutions of a mathematical model for fluid transport in peritoneal dialysis. Ukrainian Math. J. – 2005.- vol. 57. P.1112--1119.
A12. J.Waniewski, V.Dutka, J.Stachowska-Pietka, R. Cherniha. Distributed Modeling of Glucose-Induced Osmotic Flow. Advances in Peritoneal Dialysis―2007―vol.23 (part 1)―P.2―6.
A13. Cherniha R. and Pliukhin O. Symmetries and solutions of reaction-diffusion-convection equations with power diffusivities. PAMM Proc. Math.Mech.-- 2007-vol.7, P.2040065-6.
A14. Cherniha R. and Myroniuk L. Lie Symmetries and Exact Solutions of a Class of Thin Film Equations. Journal of Physical Mathematics – 2010-- Vol: 2 P. 1-19.
A15. Cherniha R. and Kovalenko S. Lie symmetry of a class of nonlinear boundary value
problems with free boundaries. Banach Center Publ. --2011. --Vol. 93. P. 95—104
A16. Cherniha R. and Pliukhin O. Nonlinear evolution equations with exponential
nonlinearities: conditional symmetries and exact solutions. Banach Center Publ. --2011. --Vol. 93. P. 105—115.
À17 J Waniewski, J Stachowska-Pietka, R Cherniha, B Lindholm DOES THE PERITONEUM SWELLS OR SHRINK DURING PERITONEAL DIALYSIS?
Nephrology Dialysis Transplantation (Oxford University Press)—2020--vol. 35, Supplement_3, gfaa142. P1158
A18 J Waniewski, J Stachowska-Pietka, R Cherniha, B Lindholm. SWELLING OF PERITONEAL TISSUE DURING PERITONEAL DIALYSIS: COMPUTATIONAL ASSESSMENT USING POROELASTIC THEORY. Nephrology Dialysis Transplantation (Oxford University Press)— 2020--vol. 36, Supplement_1, gfab101. 0016.
Last time updated: 10th January, 2022