Separation of variables in PDEs using nonlinear transformations: Applications to reaction-diffusion type equations

被引：19
|
作者：
Polyanin, Andrei D. [1 ,2 ,3 ]
Zhurov, Alexei, I [1 ,4 ]
机构：
[1] Russian Acad Sci, Ishlinsky Inst Problems Mech, 101 Vernadsky Ave,Bldg 1, Moscow 119526, Russia
[2] Natl Res Nucl Univ MEPhI, 31 Kashirskoe Shosse, Moscow 115409, Russia
[3] Bauman Moscow State Tech Univ, 5 Second Baumanskaya St, Moscow 105005, Russia
[4] Cardiff Univ, Heath Pk, Cardiff CF14 4XY, S Glam, Wales
来源：
APPLIED MATHEMATICS LETTERS | 2020年 / 100卷 / 100期
基金：
俄罗斯基础研究基金会;
关键词：
Functional separation of variables; Generalized separation of variables; Exact solutions; Nonlinear PDEs; Reaction-diffusion equations; FUNCTIONAL SEPARABLE SOLUTIONS; IMPLICIT FORM; CONSTRUCTION; DELAY;
D O I：
10.1016/j.aml.2019.106055
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper describes a new approach to constructing exact solutions of nonlinear partial differential equations that employs separation of variables using special (nonlinear integral) transformations and the splitting principle. To illustrate its effectiveness, the method is applied to nonlinear reaction-diffusion type equations that involve variable coefficients and arbitrary functions. New exact functional separable solutions as well as generalized traveling wave solutions are obtained. (C) 2019 Elsevier Ltd. All rights reserved.
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页数：7
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