**Research papers: 1996–2000**

You can download all papers listed below as total pdf file (1.76 Mb).

**1996**

Fushchych W.I., Barannyk A.F., On a new method of construction of solutions of nonlinear wave equations, Proc. Acad. of Sci. Ukraine, 1996, N 10, p.48–51 (in Ukrainian, English abstract).

Fushchych W.I., Barannyk L.L., Symmetry reduction as a method of multiplying solutions of systems of linear differential equations, Proc. Acad. of Sci. Ukraine, 1996, N 12, p.44–49 (in Ukrainian, English abstract).

Fushchych W.I., Boyko V.M., Galilei-invariant higher-order equations of Burgers and Kortewed-de Vries types, Ukrain. Math. J., 1996, V.48, N 12, p.1589–1601 (in Ukrainian, English abstract).

Fushchych W.I., Boyko V.M., Lowering the order and general solutions of some classes of equations of mathematical physics, Proc. Acad. of Sci. Ukraine, 1996, N 9, p.43–48 (in Ukrainian, English abstract).

Fushchych W.I., Cherniha R.M., Chopyk V.I., On unique symmetry of two nonlinear generalizations of the Schr\"odinger equation, J. Nonlinear Math. Phys., 1996, V.3, N 3–4, p.296–301 (in English).

Fushchych W.I., Lahno V.I., On new nonlinear equations invariant under Poincar\'e group in two-dimentional space-times, Proc. Acad. of Sci. Ukraine, 1996, N 11, p.60–65 (in Ukrainian, English abstract).

Fushchych W.I., Marko P.V., Zhdanov R.Z., Symmetry classification of multi-component scale-invariant wave equations, Preprint ASI-TPA/8/96, Arnold-Sommerfeld-Institute for Mathematical Physics, Germany, 1996, 9p. (in English).

Zhdanov R.Z., Fushchych W.I., Marko P.V., New scale-invariant nonlinear differential equations for a complex scalar field, Physica D, 1996, V.95, p.158–162 (in English).

**1997**

Basarab-Horwath P., Barannyk L.L., Fushchych W.I., Some exact solutions of a conformally invariant nonlinear Schr\"odinger equation, Preprint LiTH-MAT-R-97-11, Link\"oping University, Sweden, 1997, 12p. (in English).

Basarab-Horwath P., Fushchych W.I., Implicit and parabolic ansatzes: some new ansatzes for old equations, Proceedings of the Second International Conference "Symmetry in Nonlinear Mathematical Physics. Memorial Prof. W. Fushchych Conference" (July 7-13, 1997, Kyiv), Editors M. Shkil, A. Nikitin and V. Boyko, Kyiv, Institute Mathematics, 1997, V.1, p.34–47 (in English).

Basarab-Horwath P., Fushchych W.I., Barannyk L.F., Solutions of the relativistic nonlinear wave equation by solutions of the nonlinear Schr\"odinger equation, Reports on Mathematical Physics, 1997, V.39, N 3, p.353–374 (in English).

Basarab-Horwath P., Fushchych W.I, Roman O.V., On a new conformal symmetry for a complex scalar field, Phys. Lett. A, 1997, V.226, p.150-154 (in English).

Fushchych W.I., Symmetry of equations of linear and nonlinear quantum mechanics, Ukrain. Math. J., 1997, V.49, N 1, p.164–177 (in Ukrainian, English abstract).

Fushchych W.I., What is the velocity of electromagnetic field?, Proc. Acad. of Sci. Ukraine, 1997, N 4, p.48–53 (in Ukrainian, English abstract).

Fushchych W.I., Symmetry of equations of nonlinear quantum mechanics, Proceedings on the XXI International Colloquium on Group Theoretical Methods in Physics, Group21 "Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras" (July 15-20, 1996, Goslar, Germany), Editors: H.-H. Doebner, W. Scherer, P. Natterman, Singapore, Word Scientific, 1997, V.1, p.439–446 (in English).

Fushchych W.I., Barannyk L.L., Symmetry reduction on subalgebras of the Poincar\'e algebra of a nonlinear system of differential equations for a vector field, Proc. Acad. of Sci. Ukraine, 1997, N 8, p.50–57 (in Ukrainian, English abstract).

Fushchych W.I., Boyko V.M., Continuity equation in nonlinear quantum mechanics and the Galilei relativity principle, J. Nonlinear Math. Phys., 1997, V.4, N 1-2, p.124–128 (in English).

Fushchych W.I., Nikitin A.G., Higher symmetries and exact solutions of linear and nonlinear Schr\"odinger equation, J. Math. Phys., 1997, V.38, N 11, p.5944–5959; Preprint ASI-TPA/9/96, Arnold-Sommerfeld-Institute for Mathematical Physics, Germany, 1996, 23p. (in English).

Fushchych W.I., Serov M.I., Tulupova L.O., Conditional symmetry of the Navier-Stokes equations, Ukrain. Math. J., 1997, V.49, N 6, p.806-813 (in Ukrainian, English abstract).

Fushchych W.I., Symenoh Z.I., High-order equations of motion in quantum mechanics and Galilean relativity, J. Phys. A: Math. Gen., 1997, V.30, N 6, L131–L135 (in English).

Fushchych W.I., Symenoh Z.I., Symmetry of equations with convection terms, J. Nonlinear Math. Phys., 1997, V.4, N 3–4, p.470–479 (in English).

Fushchych W.I., Tsyfra I.M., On new Galilei- and Poincar\'e-invariant nonlinear equations for electromagnetic field, J. Nonlinear Math. Phys., 1997, V.4, N 1-2, p.44-48 (in English).

Lahno V.I., Fushchych W.I., Reduction of the self-dual Yang-Mills equations with respect to subgroups of the extended Poincar\'e group, Theor. and Math. Phys., 1997, V.100, N 3, p.329–342 (in English).

Ma W.X., Bullough R.K., Caudrey P.J., Fushchych W.I., Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras, J. Phys. A: Math. Gen., 1997, V.30, N 14, p.5141–5149 (in English).

Zhdanov R.Z., Fushchych W.I., On new representations of Galilei groups, J. Nonlinear Math. Phys., 1997, V.4, N 3–4, p.426–435 (in English).

**1998**

Barannyk L.F., Basarab-Horwath P., Fushchych W.I., On the classification of subalgebras of the conformal algebra with respect to inner automorphisms, J. Math. Phys., 1998, V.39, N 9, p.4899–4922 (in English).

Boyko V.M., Fushchych W.I., Lowering of order and general solutions of some classes of partial differential equations, Reports on Math. Phys., 1998, V.41, N 3, p.311–318 (in English).

Fushchych W.I., What is the velocity of the electromagnetic field?, J. Nonlinear Math. Phys., 1998, V.5, N 2, p.159–161 (in English).

Fushchych W.I., Lahno V.I., Linear and nonlinear representation of the Galilei groups in a two-dimensional space-time, Ukrain. Math. J., 1998, V.50, N 3, p.414–423 (in Ukrainian, English abstract).

Fushchych W.I., Serov M.I., Podoshvelev Yu.G., Conformal symmetry of a nonlinear cylindrically symmetric wave equation, Proc. Acad. of Sci. Ukraine, 1998, N 4, p.64–68 (in Ukrainian, English abstract).

Fushchych W.I., Serov M.I., Serova M.M., Gleba A.V., Lie and conditional symmetries of the Hamilton-Jacobi system of equations, Proc. Acad. of Sci. Ukraine, 1998, N 12, p.49–52 (in Ukrainian, English abstract).

Fushchych W.I., Symenoh Z.I., Tsyfra I.M., The Schr\"odinger equation with variable potential, J. Nonlinear Math. Phys., 1998, V.5, N1, p.13–22; Preprint, Department of Mathematics, Link\"oping University, Sweden, 1996, 15p. (in English).

Zhdanov R.Z., Revenko I.V., Fushchych W.I., Stationary mKdV hierarchy and integrability of the Dirac equations by quadratures, Phys. Lett. A, 1998, V.241, N 3, p.155–158 (in English).

**1999**

Fushchych W.I., Serov M.I., Podoshvelev Yu.G., Conformal invariance of a system of eikonal equations, Proc. Acad. of Sci. Ukraine, 1999, N 1, p.43–47 (in Ukrainian, English abstract).

**2000**

Zhdanov R.Z., Lahno V.I., Fushchych W.I., On
covariant realizations of the Euclid group, Comm. Math. Phys., 2000,
V.212, N 3, p.535–556 (in English).

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