Open AccessDynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping
Author(s) -
Zhijiang Du,
Xianke Lin,
Yulin Ren
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021118
Subject(s) - monotonic function , mathematics , burgers' equation , mathematical analysis , abelian group , invariant (physics) , mathematical physics , physics , pure mathematics , partial differential equation
This paper discusses the existence of solitary waves and periodic waves for a generalized (2+1)-dimensional Kadomtsev-Petviashvili modified equal width-Burgers (KP-MEW-Burgers) equation with small damping and a weak local delay convolution kernel by using the dynamical systems approach, specifically based on geometric singular perturbation theory and invariant manifold theory. Moreover, the monotonicity of the wave speed is proved by analyzing the ratio of Abelian integrals. The upper and lower bounds of the limit wave speed are given. In addition, the upper and lower bounds and monotonicity of the period \begin{document}$ T $\end{document} of traveling wave when the small positive parameter \begin{document}$ \tau\rightarrow 0 $\end{document} are also obtained. Perhaps this paper is the first discussion on the solitary waves and periodic waves for the delayed KP-MEW-Burgers equations and the Abelian integral theory may be the first application to the study of the (2+1)-dimensional equation.