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

Zengji Du; Xiaojie Lin; Yulin Ren

doi:10.3934/cpaa.2021118

Article Contents

2022, Volume 21, Issue 6: 1987-2003. Doi: 10.3934/cpaa.2021118

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

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

^*Corresponding author
^*Corresponding author

(Dedicated to Professor Goong Chen on the occasion of his 70th birthday)

Received: January 2021

Revised: June 2021

Published: June 2022

This work is partially supported by the Natural Science Foundation of China (Grant Nos. 11871251, 12090011 and 11771185)

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Abstract

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.

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Mathematics Subject Classification: Primary: 35C07; 34D15; 35B10.

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Figure 1. The homoclinic orbit within $ u\leq-\frac{3}{2a} $

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Figure 2. The graph of the function $ v(z) $

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Figure 3. The graph of the function $ v(z) $

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