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On Asymptotic Properties of Semi-relativistic Hartree Equation with combined Hartree-type nonlinearities
doi: 10.3934/cpaa.2021118
Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping
Zengji Du , , Xiaojie Lin and Yulin Ren
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
(Dedicated to Professor Goong Chen on the occasion of his 70th birthday)
Received January 2021 Revised June 2021 Early access July 2021
Fund Project: This work is partially supported by the Natural Science Foundation of China (Grant Nos. 11871251, 12090011 and 11771185)
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 $ T $ of traveling wave when the small positive parameter $ \tau\rightarrow 0 $ 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.
Keywords: KP-MEW-Burgers equation, solitary wave, periodic wave, limit wave speed, geometric singular perturbation, Abelian integrals.
Mathematics Subject Classification: Primary: 35C07; 34D15; 35B10.
Citation: Zengji Du, Xiaojie Lin, Yulin Ren. Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2021118
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Figure 1. The homoclinic orbit within $ u\leq-\frac{3}{2a} $
Figure 2. The graph of the function $ v(z) $
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Zengji Du Xiaojie Lin Yulin Ren