Painlevé Analysis and Auto-Bäcklund Transformation for a General Variable Coefficient Burgers Equation with Linear Damping Term
Year: 2024
Author: Yadong Shang, Xiaoru Zheng
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 133–141
Abstract
This paper investigates a general variable coefficient (gVC) Burgers equation with linear damping term. We derive the Painlevé property of the equation under certain constraint condition of the coefficients. Then we obtain an auto-Bäcklund transformation of this equation in terms of the Painlevé property. Finally, we find a large number of new explicit exact solutions of the equation. Especially, infinite explicit exact singular wave solutions are obtained for the first time. It is worth noting that these singular wave solutions will blow up on some lines or curves in the $(x,t)$ plane. These facts reflect the complexity of the structure of the solution of the gVC Burgers equation with linear damping term. It also reflects the complexity of nonlinear wave propagation in fluid from one aspect.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.133
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 133–141
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Painlevé property auto-Bäcklund transformation a gVC Burgers equation with linear damping term exact solutions.