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On One Method for Constructing Exact Solutions of Nonlinear Equations of Mathematical Physics

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Abstract

A new method for constructing exact solutions of nonlinear equations of mathematical physics is proposed. The method is based on nonlinear integral transformations in combination with the splitting principle. The effectiveness of the method is illustrated by nonlinear reaction–diffusion equations that involve two or three arbitrary functions. New exact functional separable solutions and generalized traveling-wave solutions are presented.

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Funding

This study was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the State Assignment (state registration nos. AAAA-A17-117021310385-6 and AAAA-A17-117021310375-7) and was supported in part by the Russian Foundation for Basic Research (project no. 18-29-10025).

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    A. D. Polyanin & A. I. Zhurov

  2. National Research Nuclear University “Moscow Engineering Physics Institute”, 115409, Moscow, Russia

    A. D. Polyanin

Authors
  1. A. D. Polyanin
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  2. A. I. Zhurov
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Corresponding authors

Correspondence to A. D. Polyanin or A. I. Zhurov.

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Translated by I. Ruzanova

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Polyanin, A.D., Zhurov, A.I. On One Method for Constructing Exact Solutions of Nonlinear Equations of Mathematical Physics. Dokl. Math. 100, 582–585 (2019). https://doi.org/10.1134/S1064562419060115

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  • DOI: https://doi.org/10.1134/S1064562419060115

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