Functional separable solutions of two classes of nonlinear mathematical physics equations

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Abstract

The study describes a new modification of the method of functional separation of variables for nonlinear equations of mathematical physics. Solutions are sought in an implicit form that involves several free functions; the specific expressions of these functions are determined in the subsequent analysis of the arising functional differential equations. The effectiveness of the method is illustrated by examples of nonlinear reaction-diffusion equations and Klein-Gordon type equations with variable coefficients that depend on one or more arbitrary functions. A number of new exact functional separable solutions and generalized traveling-wave solutions are obtained.

About the authors

A. D. Polyanin

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)

Email: polyanin@ipmnet.ru
Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526; 31, Kashirskoe shosse, Moscow, 115409

A. I. Zhurov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: zhurov@ipmnet.ru
Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526

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