2017
Том 69
№ 9

All Issues

Application of one constructive method for the construction of non-Lie solutions of nonlinear evolution equations

Cherniga R. M.

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Abstract

We propose a constructive method for the construction of exact solutions of nonlinear partial differential equations. The method is based on the investigation of a fixed nonlinear partial differential equation (system of partial differential equations) together with an additional condition in the form of a linear ordinary differential equation of higher order. By using this method, we obtain new solutions for nonlinear generalizations of the Fisher equation and for some nonlinear evolution systems that describe real processes in physics, biology, and chemistry.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 6, pp 910-924.

Citation Example: Cherniga R. M. Application of one constructive method for the construction of non-Lie solutions of nonlinear evolution equations // Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 814–827.

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