Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
type: Item
instance of: scholarly article
title: Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
zbMATH Open document ID: 0863.35106
DOI: 10.1016/0020-7462(95)00064-X
author: Wen-Xiu Ma
author: Benno Fuchssteiner
published in: International Journal of Non-Linear Mechanics
publication date: 1997-01-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/solv-int/9511005
review text: The paper deals with explicit traveling wave solutions of the Kolmogorov-Petrovskii-Piskunov equation \[ u_t-u_{xx}+\mu u+\nu u^2+\delta u^3=0,\tag{1} \] where \(\mu\), \(\nu\), \(\delta\) are real constants. The authors decompose the equation (1) into two problems and solve these problems, in order to analyze the possibilities of solutions corresponding to two Riccati equations as well as to give explicitly the number of exact solutions of (1). In the further investigations, the authors use Cole-Hopf transformation and Bäcklund transformation.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 966572
zbMATH Keywords: explicit traveling wave solutions of the Kolmogorov-Petrovskii-Piskunov equation
zbMATH Keywords: Riccati equations
zbMATH Keywords: number of exact solutions
zbMATH Keywords: Cole-Hopf transformation
zbMATH Keywords: Bäcklund transformation
Wikidata QID: Q56525654
reviewed by: Emil Minchev
MaRDI profile type: Publication
arXiv ID: solv-int/9511005
OpenAlex ID: W3099839123
description: scientific article