Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation

Xiaowan Li; Zengji Du; Shuguan Ji

doi:10.3934/cpaa.2019132

Article Contents

2019, Volume 18, Issue 6: 2961-2981. Doi: 10.3934/cpaa.2019132

This issue Previous Article Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth Next Article Asymptotic spreading for a time-periodic predator-prey system

Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation

1.
School of Mathematics, Jilin University, Changchun, Jilin 130012, China
2.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
3.
School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, Jilin 130024, China

^* Corresponding author
^* Corresponding author

Received: July 31, 2018

Revised: December 31, 2018

Published: May 2019

This work is supported by the Natural Science Foundation of China (Grant Nos. 11871251, 11771185, 11671071 and 11871140), the Fundamental Research Funds for the Central Universities at Jilin University (no. 2017TD–18), and the Special Funds of Provincial Industrial Innovation in Jilin Province (no. 2017C028–1)

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Abstract

This paper is concerned with the Camassa-Holm-KP equation, which is a model for shallow water waves. By using the analysis of the phase space, we obtain some qualitative properties of equilibrium points and existence results of solitary wave solutions for the Camassa-Holm-KP equation without delay. Furthermore we show the existence of solitary wave solutions for the equation with a special local delay convolution kernel by combining the geometric singular perturbation theory and invariant manifold theory. In addition, we discuss the existence of solitary wave solutions for the Camassa-Holm-KP equation with strength $ 1 $ of nonlinearity, and prove the monotonicity of the wave speed by analyzing the ratio of the Abelian integral.

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Mathematics Subject Classification: Primary: 35Q53, 35L05, 74J35, 34D15.

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Figure 1. The phase portraits of system (19) for n is odd

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Figure 2. The phase portraits of system (19) for n is even

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