**Research papers: 1986–1989**

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**1986**

Barannyk A.F., Fushchych W.I., On continuous subgroups of pseudoorthogonal and pseudounitary groups, Preprint N 86.77, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1986, 48p. (in Russian).

Barannyk L.F., Barannyk A.F., Fushchych W.I., On continuous subgroups of the generalized Poincaré group P(1,n), in: Group-Theoretical Methods in Physics, Proc. of Third Internat. Seminar, Jurmala, 1985, Moscow, Nauka, 1986, V.2, p.169–176 (in Russian).

Barannyk L.F., Fushchych W.I., Casimir operators for the generalized Poincaré groups and Galilean group, in: Group-Theoretical Methods in Physics, Proc. of Third Internat. Seminar, Jurmala, 1985, Moscow, Nauka, 1986, V.2, p.176–183 (in Russian).

Barannyk L.F., Fushchych W.I., Invariants of subgroups of the generalized Poincaré group P(1,n), Preprint N 86.86, Kyiv, Inst. of Math. Acad. of Sci. Ukraine, 1986, 40p. (in Russian).

Fushchych W.I., On symmetry and exact solutions of some multidimensional equations of mathematical physics, in: Investigations on theory of functions of complex variable with application to mechanics of continua, Kyiv, Naukova Dumka, 1986, p.146–160 (in Russian).

Fushchych W.I., Barannyk A.F., Barannyk L.F., Continuous subgroups of the generalized Euclidean group, Ukrain. Math. J., 1986, V.38, N 1, p.67–72 (in Russian).

Fushchych W.I., Cherniha R.M., On exact solutions of two multidimensional equations of Schrödinger type, Preprint N 86.16, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1986, 44p. (in Russian).

Fushchych W.I., Fedorchuk V.M., Fedorchuk I.M., Subgroup structure of generalized Poincaré group and exact solutions of some nonlinear wave equations, Preprint N 86.27, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1986, 36 p. (in Russian).

Fushchych W., Shtelen W., Zhdanov R. Conformally invariant generalizations of Dirac-Heisenberg equation and their exact solutions, in: Group-Theoretical Methods in Physics, Proc. of Third Internat. Seminar, Jurmala, 1985, Moscow, Nauka, 1986, V.1, p.497–501 (in Russian).

Fushchych W.I., Slavutskii S.L., On nonlinear Galilei-invariant generalization of Lamé equation, Proc. Acad. of Sci. of USSR (DAN SSSR), 1986, V.237, N 2, p.320–323 (in Russian).

Fushchych W.I., Slavutskii S.L., On symmetry of some equations of motion of ideal fluid, in: Investigations on theory of functions of complex variable with application to mechanics of continua, Kyiv, Naukova dumka, 1986, p.161–165 (in Russian).

Fushchych W.I., Tsyfra I.M., Conformally-invariant
nonlinear equations for electromagnetic field, in: Group-Theoretical
Methods in Physics, Proc. of Third Internat. Seminar, Jurmala, 1985, Moscow,
Nauka, 1986, V.1, p.501–505 (in Russian).

**1987**

Barannyk L.F., Fushchych W.I., On subalgebras of the Lie algebra of the extended Poincaré group P(1,n), J. Math. Phys., 1987, V.27, N 7, p.1445–1458 (in English).

Fushchych W.I., The symmetry and some exact solutions of some multi-dimensional nonlinear equations of mathematical physics, in: Proceedings of XV-th International Conference on Differential Geometric Methods in Theoretical Physics, Eds. H.-D. Doebner and J.D. Hennig, World Scientific, Singapore - New Jersey - Hong Kong, 1987, p.544–549 (in English).

Fushchych W.I., How to extend symmetry of differential equations?, in Symmetry and Solutions of Nonlinear Equations of Mathematical Physics, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1987, p.4–16 (in Russian).

Fushchych W.I., On symmetry and exact solutions of multi-dimensional nonlinear wave equations, Ukrain. Math. J., 1987, V.39, N 1, p.116–123 (in Russian).

Fushchych W., Krivsky I., Simulik V., On vector Lagrangians for electromagnetic and spinor field, Preprint N 87.54, Kyiv, Inst. of Math. Acad Sci. of Ukr., 1987 (in Russian, English abstract).

Fushchych W.I., Nikitin A.G., On the new invariance algebras and superalgebras of relativistic wave equations, J. Phys. A: Math. and Gen., 1987, V.20, p.537–549 (in English).

Fushchych W.I., Serov N.I., On some exact solutions of three-dimensional non-linear Schrödinger equation, J. Phys. A: Math. Gen., 1987, V.20, L929–L933 (in English).

Fushchych W., Shtelen W., On reduction and solutions of nonlinear Dirac equation, Teoreticheskaya i Matematicheskaya Fizika (Theor. Math. Phys.), 1987, V.72, N 1, p.35–44 (in Russian, English abstract).

Fushchych W.I., Tsyfra I.M., On a reduction and solutions of the nonlinear wave equations with broken symmetry, J. Phys. A: Math. Gen., 1987, V.20, L45–L48 (in English).

Fushchych W.I., Zhdanov R.Z., On some generalization of the method of separation of variables for systems of linear differential equations, in Symmetry and Solutions of Nonlinear Equations of Mathematical Physics, Kyiv, Inst. of Math. Acad. of Sci. Ukraine, 1987, p.17–22 (in Russian).

Fushchych W.I., Zhdanov R.Z., On
some exact solution of a system of nonlinear differential equations for
spinor and vector fields, J. Phys. A: Math. Gen., 1987, V.20, p.4173–4190
(in English).

**1988**

Barannyk L.F., Fushchych W.I., On continuous subgroups of the conformal group of the Minkowski space $R_{1,n}$, Preprint N 88-34, Kyiv, Inst. of Math. Acad. of Sci. Ukraine, 1988, 48p. (in Russian).

Fushchych W.I., Exact solutions of multidimansional Dirac's and Schrodinger's equations, Preprint N 467, Inst. for Math. and Appl., Minneapolis, 1988, 14p. (in English).

Barannyk L.F., Lahno V.I., Fushchych W.I., Subalgebras of the Poincar\'e algebra $AP(2,3)$ and symmetry reduction of nonlinear ultrahyperbolic d'Alambert equation. I, Ukrain. Math. J., 1988, V.40, N 4, p.411–416 (in Russian).

Fushchych W.I., Galitsyn A.S., Polubinskii A.S., A new mathematical model of diffusion processes with finite velocity, Proc. Acad. of Sci. Ukraine, 1988, N 8, p.21–26 (in Ukrainian, English abstract).

Fushchych W., Krivsky I., Simulik V., On vector and pseudovector Lagrangians for electromagnetic field, Preprint N 466, Inst. for Math. and Appl., Minneapolis, 1988, 6p. (in English).

Fushchych W.I., Serov N.I., Conditional invariance and exact solutions of a nonlinear acoustics equation, Proc. Acad. of Sci. Ukraine, 1988, N 10, p.27–31 (in Russian, English abstract).

Fushchych W.I., Serov N.I., On conditional invariance of the nonlinear d'Alembert, Born-Infeld, Monge-Ampere equations under conformal algebra, in Symmetry Analysis and Solutions of Mathematical Physics Equations, Kyiv, Inst. of Math. Acad. of Sci. Ukraine, 1988, p.98–102 (in Russian).

Fushchych W.I., Serov N.I., Chopyk V.I., Conditional invariance and nonlinear heat equations, Proc. Acad. of Sci. Ukraine, 1988, N 9, p.17-20 (in Russian, English abstract).

Fushchych W.I., Yehorchenko I.A., On symmetry properties of complex-valued non-linear wave equations, Proc. Acad. of Sci. of USSR (DAN SSSR), 1988, V.298, N 2, p.347–351 (in Russian).

Fushchych W.I., Zhdanov R.Z., On the reduction and some new exact solutions of the nonlinear Dirac and Dirac-Klein-Gordon equation, J. Phys. A: Math. Gen., 1988, V.21, N 1, L5–L9 (in English).

Fushchych W.I., Zhdanov R.Z., Nonlocal Ansatze for the Dirac equation, J. Phys. A: Math. Gen., 1988, V.21, N 23, L1117–L1121 (in English).

Fushchych W.I., Zhdanov R.Z., On some new exact solutions of nonlinear d'Alembert and Hamilton equations, Preprint N 468, Minneapolis, Inst. for Math. and Appl., 1988, 5p. (in English).

Fushchych W.I., Zhdanov R.Z., Symmetry
and exact solutions of the nonlinear Dirac equation, Fizika Elementar.
Chastits i Atom.Yadra (Sov. J. Part. Nucl.), 1988, V.19, N 5, p.1154–1196
(in Russian, English abstract).

**1989**

Barannyk A.F., Moskalenko Yu.D., Fushchych W.I., Subalgebras of the affine algebra AIGL(3,R), Preprint N 89-65, Kyiv, Inst. of Math. Acad. of Sci. Ukraine, 1989, 32p. (in Russian)

Barannyk A.F., Moskalenko Yu.D., Fushchych W.I., Subalgebras of the pseudoorthogonal group AO(3,3), Preprint N 89-67, Kyiv, Inst. of Math. Acad. of Sci. Ukraine, 1989, 40p. (in Russian)

Barannyk L.F., Fushchych W.I., Continuous subgroups of the generalized Schrodinger group, J. Math. Phys., 1989, V.29, N 2, p.280–290 (in English).

Barannyk L.F., Lahno V.I., Fushchych W.I., Subalgebras of the Poincar\'e algebra $AP(2,3)$ and symmetry reduction of nonlinear ultrahyperbolic d'Alambert equations. II, Ukrain. Math. J., 1989, V.41, N5, p.579–584 (in Russian).

Fushchych W.I., Galilei relativity principle and nonlinear partial differential equations, in Abstracts of the All-Union Conference ``Nonlinear Problems of Differential Equations and Mathematical Physics'', September 12-15, 1989, Ternopil', Ukpaine, Part II, p.444–452 (in Russian).

Fushchych W.I., Cherniha R.M., Galilei-invariant nonlinear equations of Schr\"odingertype and their exact solutions. I, Ukrain. Math. J., 1989, V.41, N10, p.1349–1357 (in Russian).

Fushchych W.I., Cherniha R.M., Galilei-invariant nonlinear equations of Schr\"odingertype and their exact solutions. II, Ukrain. Math. J., 1989, V.41, N12, p.1687–1694 (in Russian).

Fushchych W.I., Kornyak V.V., Computing algebra application for determining Lie and Lie-B\"acklund symmetries of differential equations, J. Symbolic Computation, 1989, V.7, N8, p.611–619 (in English).

Fushchych W.I., Krivsky I.Yu., Simulik V.M., On vector and pseudovector Lagrangians for the electromagnetic field, Nuovo Cim. B, 1989, V.103, N4, p.423–429 (in English).

Fushchych W.I., Krivsky I.Yu., Simulik V.M., Non-Lie symmetries and Noetherian analysis of conservation laws for Dirac equation, Preprint N 89-49, Kyiv, Inst. of Math. Acad. of Sci. Ukraine, 1989, 39p. (in Russian)

Fushchych W.I., Nikitin A.G., On new systems and conservation laws for elastic waves, Proc. Acad. of Sci. of USSR (DAN SSSR), 1989, V.304, N2, p.333–335 (in Russian).

Fushchych W.I., Revenko I.V., On exact solutions of Lorentz-Maxwell's equations, Proc. Acad. of Sci. Ukraine, 1989, N6, p.27–31 (in Ukrainian, English abstract).

Fushchych W.I., Revenko I.V., Poincar\'e-invariant equations of third- and forth-order in Ostrogradskii mechanics, Proc. Acad. of Sci. Ukraine, 1989, N11, p.25–28 (in Ukrainian, English abstract).

Fushchych W.I., Serov N.I., Conditional invariance and exact solutions of the Boussinesq equation, in Symmetry and solutions of equations of mathematical physics, Kyiv, Inst. of Math. Acad. of Sci. of Ukraine, 1989, p.95–102 (in Russian).

Fushchych W.I., Shtelen W.M., On approximate symmetry and approximate solutions of non-linear wave equation with a small parameter, J. Phys. A: Math. Gen., 1989, 22, L887–L890 (in English).

Fushchych W.I., Yehorchenko I.A., Differential invariants of the Galilei algebra, Proc. Acad. of Sci. Ukraine, 1989, N4, p.29–32 (in Russian, English abstract).

Fushchych W.I., Yehorchenko I.A., Differential invariants of the Poincare and conformal algebra, Proc. Acad. of Sci. Ukraine, 1989, N5, p.21–22 (in Ukrainian, English abstract).

Fushchych W.I., Yehorchenko I.A., The symmetry and exact solutions of the non-linear d'Alembert equations for complex fields, J. Phys. A: Math. Gen., 1989, V.22, p.2643–2652 (in English).

Fushchych W.I., Zhdanov R.Z., On some new exact solutions of the nonlinear d'Alembert-Hamilton system, Phys. Lett. A, 1989, V.141, N3-4, p.113–115 (in English).

Fushchych W.I., Zhdanov R.Z., Symmetry and exact solutions of nonlinear spinor equations, Phys. Repts., 1989, V.172, N4, p.123–174 (in English).

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