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

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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.

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Authors
  1. R. M. Cherniha
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To the blessed memory of V. I. Fushchich

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 814–827, June, 1997.

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Cherniha, R.M. Application of one constructive method for the construction of non-Lie solutions of nonlinear evolution equations. Ukr Math J 49, 910–924 (1997). https://doi.org/10.1007/BF02513431

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  • DOI: https://doi.org/10.1007/BF02513431

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