**Research papers: 1990–1992**

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**1990**

Barannyk A.F., Barannyk L.F., Fushchych W.I., Reduction and exact solutions of Hamilton-Jacobi equation, Preprint N 90.41, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1990, 40p. (in Russian).

Fushchych W.I., On a generalization of S. Lie method, in Algebraic-Theoretical Analysis of Equations of Mathematical Physics, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1990, p.4–9 (in Russian).

Fushchych W.I., On some new wave equations of mathematical physics, in Algebraic-Theoretical Analysis of Equations of Mathematical Physics, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1990, p.9–11 (in Russian).

Fushchych W.I., Barannyk A.F., On exact solutions of nonlinear d'Alembert equation in Minkowski space R(1,n), Proc. Acad. of Sci. Ukraine, 1990, N 6, p.31–34 (in Russian, English abstract).

Fushchych W.I., Barannyk A.F., Maximal subalgebras of (n-1) range of algebra AP(1,n) and reduction of nonlinear wave equation. I, Ukrain. Math. J., 1990, V.42, N 11, p.1552–1559 (in Russian).

Fushchych W.I., Barannyk A.F., Maximal subalgebras of (n-1) range of algebra AP(1,n) and reduction of nonlinear wave equation. II, Ukrain. Math. J., 1990, V.42, N 12, p.1693–1700 (in Russian).

Fushchych W.I., Barannyk A.F., Moskalenko Yu., On exact solutions of d'Alembert and Liouville equations in pseudoeuclidean space $R_{2,2}$. I, Ukrain. Math. J., 1990, V.42, N8, p.1122–1128 (in Russian).

Fushchych W.I., Barannyk A.F., Moskalenko Yu., On exact solutions of d'Alembert and Liouville equations in pseudoeuclidean space $R_{2,2}$. II, Ukrain. Math. J., 1990, V.42, N9, p.1237–1244 (in Russian).

Fushchych W.I., Chopyk V.I., Conditional invariance of the nonlinear Schrodinger equations, Proc. Acad. of Sci. Ukraine, 1990, N4, p.30–33 (in Russian, English abstract).

Fushchych W.I., Chopyk V.I., Myronyuk P.I., Conditional invariance and exact solutions of the three-dimensional nonlinear acoustics equation, Proc. Acad. of Sci. Ukraine, 1990, N9, p.25–28 (in Russian, English abstract).

Fushchych W., Galitsyn A., Polubinskii A., On a new mathematical model of processes of heat conductivity, Ukrain. Math. J., 1990, V.42, N2, p.237–245 (in Russian).

Fushchych W.I., Nikitin A.G., On superalgebras of symmetry operators of relativistic wave equations, Selected Topics in QFT and Mathematical Physics, Proceedings of the 5th International conference (Liblice, Czechoslovakia, June 25–30, 1989), Editors J. Niederle and J. Fisher, World Scientific, 1990, p.385–391 (in English).

Fushchych W.I., Nikitin A.G., On the new constants of motion for two- and three-particle equations, J. Phys. A: Math. and Gen., 1990, V.23, N11, L533–L535 (in English).

Fushchych W.I., Serov N.I., Conditional invariance and reduction of the nonlinear heat equation, Proc. Acad. of Sci. Ukraine, 1990, N7, p.24–27 (in Russian, English abstract).

Fushchych W., Serov N., Amerov T., Conditional invariance of nonlinear heat equation, Proc. Acad. of Sci. Ukraine, 1990, N11, p.16–18 (in Russian, English abstract).

Fushchych W., Shtelen W., Merons and instantons as products of selfinteraction of the Dirac-G\"ursey spinor field, J. Phys. A: Math. Gen., 1990, V.23, N 10, L517–L520 (in English).

Fushchych W., Shtelen W., Spichak S., On connection between solutions of Dirac and Maxwell equations. Supersymmetry of Dirac equation, Proc. Acad. of Sci. Ukraine, 1990, N3, p.36–40 (in Russian, English abstract).

Fushchych W.I., Shtelen W.M., Zhdanov R.Z., On exact solutions of a nonlinear equation for the spinor field, in Modern Group Analysis: Methods and Applications. Some problems of modern physics, Editor A.V. Flegontov, Inst. of Informatics and Automatization, Leningrad, 1990, p.22–30 (in Russian).

Fushchych W.I., Tychynin V.A., Exact solutions and superposition principle for a nonlinear wave equation, Proc. Acad. of Sci. Ukraine, 1990, N5, p.32–36 (in Ukrainian, English abstract).

Fushchych W.I., Yehorchenko I.A., On the reduction of the multidimensional wave equation to two-dimensional equations, Proc. Acad. of Sci. Ukraine, 1990, N8, p.31–33 (in Ukrainian, English abstract).

Fushchych W.I., Zhdanov R.Z., Non-Lie Ans\"atze and exact solutions of the nonlinear spinor equation, Ukrain. Math. J., 1990, V.42, N7, p.958–962 (in Russian).

Fushchych W.I., Zhdanov R.Z., Revenko I.V., Compatibility and solutions of the nonlinear d'Alembert and Hamilton equations, Preprint N90-39, Inst. of Math. Acad. of Sci. Ukraine, Kyiv, 1990, 65p. (in Russian).

Parasyuk I.O., Fushchych W.I., Qualitative
analysis of families of bounded solutions of the nonlinear three-dimensional
Schr\"odinger equation, Ukrain. Math. J., V.42, N10, p.1344–1350 (in
Russian).

**1991**

Barannyk A.F., Barannyk L.F., Fushchych W.I., Reduction
and exact solutions of eikonal equation, Ukrain. Math. J., 1991, V.43,
N 4, p.461–474 (in Russian).

Barannyk A.F., Barannyk L.F., Fushchych W.I., Connected subgroups of the conformal group C(1,4), Ukrain. Math. J., 1991, V.43, N 7–8, p.870–884 (in Russian).

Barannyk A.F., Barannyk L.F., Fushchych W.I., Reduction of the nonlinear multidimensional Poincar\'e-invariant equation to two-dimensional equations, Ukrain. Math. J., 1991, V.43, N 10, p.1311–1323.

Barannyk A.F., Marchenko V.A., Fushchych W.I., On the reduction and exact solutions of the nonlinear multidimensional Schr\"odinger equations, Theor. Math. Phys., 1991, V.87, N 2, p.220–234 (in Russian, English abstract).

Bedrij O., Fushchych W.I., On the electromagnetic structure of elementary patricles masses, Proc. Acad. of Sci. Ukraine, 1991, N 2, p.38–40.

Fushchych W.I., Conditional symmetry of mathematical physics equations, Ukrain. Math. J., 1991, V.43, N 11, p.1456–1470 (in Russian).

Fushchych W.I., Myronyuk P.I., Conditional symmetry and exact solutions of nonlinear acoustics equation, Proc. Acad. of Sci. Ukraine, 1991, N 6, p.23–29 (in Russian).

Fushchych W.I., Parasyuk I.O., Qualitative analysis of families of bounded solutions of the multidimensional nonlinear Schr\"odinger equation, Ukrain. Math. J., 1991, V.43, N 6, p.821–828 (in Russian).

Fushchych W.I., Repeta V.K., Exact solutions of some gas dynamics and nonlinear acoustics equations, Proc. Acad. of Sci. Ukraine, 1991, N 8, p.39–45 (in Russian, English abstract).

Fushchych W., Serov N., Conditional invariance of nonlinear wave equation, Ukrain. Math. J., 1991, V.43, N 3, p.394–399 (in Russian).

Fushchych W., Serov N., Nongroup symmetry of some nonlinear wave equations, Proc. Acad. of Sci. Ukraine, 1991, N 9, p.45–49 (in Russian, English abstract).

Fushchych W.I., Serov N.I., Amerov T., On conditional symmetry of a generalized Korteweg-de Vries equation, Proc. Acad. of Sci. Ukraine, 1991, N 12, p.15–18 (in Russian, English abstract).

Fushchych W.I., Serov N.I., Repeta V.K., Conditional symmetry, reduction and exact of a nonlinear wave equation, Proc. Acad. of Sci. Ukraine, 1991, N 5, p.29–34 (in Russian, English abstract).

Fushchych W., Serov N., Repeta V., Non-Lie symmetry and exact solutions of one-dimensional gas dynamics equations, Proc. Acad. of Sci. Ukraine, 1991, N 11, p.27–33 (in Russian, English abstract).

Fuchchych W., Shtelen W., Are Maxwell's equations invariant under the Galilei transformations? Proc. Acad. of Sci. Ukraine, 1991, N 3, p.23–27 (in Ukrainian, English abstract).

Fuchchych W., Shtelen W., Slavutsky S.L., Reduction and exact solutions of the Navier-Stokes equations, J. Phys. A: Math. Gen., 1991, V.24, p.971–984 (in English).

Fuchchych W., Shtelen W., Spichak S., On the connection between solutions of Dirac an Maxwell equations, dual Poincar\'e invariance and superalgebras of invariance and solutions of nonlinear Dirac equations, J. Phys. A: Math. Gen., 1991, V.24, p.1683–1698 (in English).

Fushchych W.I., Yegorchenko I.A., Reduction and solutions of nonlinear equations for vector field, Proc. Acad. of Sci. Ukraine, 1991, N 4, p.23–25 (in Russian, English abstract).

Fushchych W.I., Yegorchenko I.A., Non-Lie ans\"atze and conditional symmetry of nonlinear Schr\"odinger equation, Ukrain. Math. J., 1991, V.43, N 12, p.1620–1628 (in Russian).

Fushchych W.I., Revenko I.V., Zhdanov R.Z., Non-symmetry approach to construction of exact solutions of a nonlinear wave equation, Proc. Acad. of Sci. Ukraine, 1991, N 7, p.15–19 (in Russian, English abstract).

Fushchych W.I. and Zhdanov R.Z., On non-Lie reduction of the nonlinear Dirac equation, J. Math. Phys., 1991, V.32, N 12, p.3488–3490 (in English).

Fushchych W.I., Zhdanov R.Z., Revenko I.V., General solutions of the nonlinear wave and eikonal equations, Ukrain. Math. J., 1991, V.43, N 11, p.1364–1379 (in Russian).

Fushchych W.I., Zhdanov R.Z., Revenko I.V., General solution of the nonlinear wave equation and of the eikonal equation, Proc. Acad. of Sci. Ukraine, 1991, N 10, p.29–31 (in Russian, English abstract).

Fushchych W.I., Zhdanov R.Z., Yegorchenko I.A., On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton system, J. Math. Anal. and Appl., 1991, V.161, N 2, p.352–360 (in English).

Nikitin A.G., Fushchych W.I., Non-Lie constants of motion for particles of arbitrary spin and systems of coupled particles, Theor. Math. Phys., 1992, V.88, N 3, p.406–415 (in Russian, English abstract).

Zhdanov R.Z., Fushchych W.I., On
the non-Lie symmetry of a Galilei-invariant equation for a particle with
the spin *s*=1/2, Theor. Math. Phys., 1991, V.89, N 3, p.413–419
(in Russian, English abstract).

**1992**

Basarab-Horwath P., Fushchych W.I., Serov M.I.,
A
simple method of finding solutions of the nonlinear d'Alembert equation,
J. Phys. A: Math. Gen., 1992, V.25, L871–L877 (in English).

Fushchych W.I., Symmetry analysis. Preface, in Symmetry Analysis of Equations of Mathematical Physics, Kiev, Inst. of Math., 1992, p.5–6 (in English).

Fushchych W.I., Conditional symmetry of equations of nonlinear mathematical physics, in Symmetry Analysis of Equations of Mathematical Physics, Kiev, Inst. of Math., 1992, p.7–27 (in English).

Fushchych W.I., New
nonlinear equation for electromagnetic field having the velocity different
from *c*, Proc. Acad. of Sci. Ukraine, 1992, N 1, p.24–27
(in English, Russian abstract).

Fushchych W.I., Nikitin A.G., The complete set of conservation laws for the electromagnetic field, J. Phys. A: Math. and Gen., 1992, V.25, N 5, L231–L233 (in English).

Fushchych W.I., Popovych R.O., Symmetry reduction of the Navier-Stokes equations to linear two-dimensional systems of equations, Proc. Acad. of Sci. Ukraine, 1992, N 8, p.29–36 (in English, Ukrainian abstract).

Fushchych W.I., Serov M.I., Amerov T.K., On nonlocal ans\"atzes for a nonlinear one-dimensional heat equation, Proc. Acad. Sci. of Ukraine, 1992, N 1, p.26–30 (in Russian, English abstract).

Fushchych W.I., Serov M.I., Amerov T.K., Conditional invariance and exact solutions of gas dynamics equations, Proc. Acad. of Sci. Ukraine, 1992, N 5, p.35–40 (in English, Russian abstract).

Fushchych W.I., Serov M.I., Tychynin V.A., Amerov T.K., On non-local symmetry of nonlinear heat equation, Proc. Acad. of Sci. Ukraine, 1992, N 11, p.27–33 (in English, Russian abstract).

Fushchych W.I., Serov M.I., Vorob'eva A.I., Conditional symmetry and exact solutions of equations of nonstationary filtration, Proc. Acad. Sci. of Ukraine, 1992, N 6, p.20–24 (in English, Ukrainain abstract).

Fushchych W.I., Shtelen W.M., Popovych R.O., On reduction of the Navier-Stokes equation to a linear heat equation, Proc. Acad. of Sci. Ukraine, 1992, N 2, p.23–30 (in Ukrainian).

Fushchych W.I., Shtelen W.M., Serov M.I., Popovych R.O.,
*Q*-conditional
symmetry of the linear heat equation, Proc. Acad. of Sci. Ukraine,
1992, N 12, p.28–33 (in English, Russian abstract).

Fushchych W.I., Tychynin V.A., Generating solutions for nonlinear equations by the Legendre transformation, Proc. Acad. of Sci. Ukraine, 1992, N 7, p.20–25 (in English, Russian abstract).

Fushchych W.I, Tychynin V.A, Nonlocal symmetry and generating solutions for Harry-Dym type equations, Proc. Acad. of Sci. Ukraine, 1992, N 9, p.24–30 (in English, Russian abstract).

Fushchych W.I., Tychynin V.A., Serov M.I., Formula of generating solutions for the Korteweg-de Vries equation, Ukrain. Math. J., 1992, V.44, N 5, p.716–719 (in Russian).

Fushchych W.I., Yegorchenko I.A., Second-order
differential invariants of the rotation group *O*(*n*) and of
its extensions: *E*(*n*), *P*(1,*n*), *G*(1,*n*),
Acta Appl. Math., 1992, V.28, p.69–92 (in English).

Fushchych W.I., Zhdanov R.Z., Conditional symmetry and reduction of partial differential equations, Ukrain. Math. J., 1992, V.44, N 7, p.875–886 (in English).

Fushchych W.I., Zhdanov R.Z., Revenko I.V., On the general solution of the d'Alembert equation with nonlinear eikonal constraint, in Symmetry Analysis of Equations of Mathematical Physics, Kiev, Institute of Mathematics, 1992, p.68–90 (in English).

Fushchych W.I., Zhdanov R.Z., Smalij V.F., On the new exact solutions of the nonlinear Maxwell-Born-Infeld equations, Proc. Acad. of Sci. Ukraine, 1992, N 10, p.28–33 (in English, Russian abstract).

Nikitin A.G., Fushchych W.I., Onufryichuk S.P., Higher symmetries of the Schr\"odinger equation, Theor. Math. Phys., 1992, V.91, N 2, p.268–278 (in Russian, English abstract).

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