On One Method for Constructing Exact Solutions
of Nonlinear Equations of Mathematical Physics
A. D. Polyanina,b,* and A. I. Zhurova,**
a Ishlinsky Institute for Problems in Mechanics,
Russian Academy of Sciences, Moscow, 119526 Russia
b National Research Nuclear University “Moscow Engineering Physics Institute,” Moscow, 115409 Russia
Correspondence to: *e-mail: polyanin@ipmnet.ru
Correspondence to: **e-mail: zhurov@ipmnet.ru
Received 21 May, 2019
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.
DOI: 10.1134/S1064562419060115