Email this article Functional separable solutions of two classes of nonlinear mathematical physics equations
- Authors: Polyanin A.D.1,2, Zhurov A.I.1
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
- Issue: Vol 486, No 3 (2019)
- Pages: 287-291
- Section: Mathematical physics
- URL: https://journals.eco-vector.com/0869-5652/article/view/13463
- DOI: https://doi.org/10.31857/S0869-56524863287-291
- ID: 13463
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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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