Open AccessFunctional separable solutions of two classes of nonlinear mathematical physics equations
Author(s) -
Andrei D. Polyanin,
Alexei I. Zhurov
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524863287-291
Subject(s) - nonlinear system , separable space , mathematics , traveling wave , differential equation , type (biology) , variable (mathematics) , reaction–diffusion system , mathematical analysis , physics , quantum mechanics , ecology , biology
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.