Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> of traveling wave when the small positive parameter <inline-formula><tex-math id="M2">\begin{document}$ \tau\rightarrow 0 $\end{document}</tex-math></inline-formula> 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.</p>