Approximate Analytical Solution of the Generalized Kolmogorov-Petrovsky-Piskunov Equation with Cubic Nonlinearity

被引：2

作者：

Zhang, Wei-guo ^{[1
]}

Hu, Xie-kui ^{[1
]}

Ling, Xing-qian ^{[1
]}

Li, Wen-xia ^{[1
]}

机构：

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2023年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

reaction-diffusion equation; approximate analytical solution; error estimation; dynamical system approach; REACTION-DIFFUSION EQUATIONS; SOLITARY-WAVE SOLUTIONS; GLOBAL STABILITY; EXPLICIT; FRONTS; TERMS; MODEL;

D O I：

10.1007/s10255-023-1054-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the approximate analytical oscillatory solutions to the generalized Kolmogorov-Petrovsky-Piskunov equation (gKPPE for short) are discussed by employing the theory of dynamical system and hypothesis undetermined method. According to the corresponding dynamical system of the bounded traveling wave solutions to the gKPPE, the number and qualitative properties of these bounded solutions are received. Furthermore, pulses (bell-shaped) and waves fronts (kink-shaped) of the gKPPE are given. In particular, two types of approximate analytical oscillatory solutions are constructed. Besides, the error estimations between the approximate analytical oscillatory solutions and the exact solutions of the gKPPE are obtained by the homogeneity principle. Finally, the approximate analytical oscillatory solutions are compared with the numerical solutions, which shows the two types of solutions are similar.

引用

页码：424 / 449

页数：26

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