Functional Separable Solutions of Two Classes of Nonlinear Mathematical Physics Equations
- Authors: Polyanin A.D.1,2, Zhurov A.I.1,2
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
- National Research Nuclear University “MEPhI”
- Issue: Vol 99, No 3 (2019)
- Pages: 321-324
- Section: Mathematical Physics
- URL: https://journals.rcsi.science/1064-5624/article/view/225686
- DOI: https://doi.org/10.1134/S1064562419030128
- ID: 225686
Cite item
Abstract
This 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 (specific expressions for these functions are determined by analyzing 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,Russian Academy of Sciences; National Research Nuclear University “MEPhI”
Author for correspondence.
Email: polyanin@ipmnet.ru
Russian Federation, Moscow, 119526; Moscow, 115409
A. I. Zhurov
Ishlinsky Institute for Problems in Mechanics,Russian Academy of Sciences; National Research Nuclear University “MEPhI”
Author for correspondence.
Email: zhurov@ipmnet.ru
Russian Federation, Moscow, 119526; Moscow, 115409