Electron. J. Differential Equations, Vol. 2017 (2017), No. 48, pp. 1-12.

Perturbational self-similar solutions for multi-dimensional Camassa-Holm-type equations

Hongli An, Mankam Kwong, Manwai Yuen

In this article, we sutdy a multi-component Camassa-Holm-type system. By employing the characteristic method, we obtain a class of perturbational self-similar solutions with elliptical symmetry, whose velocity components are governed by the generalized Emden equations. In particular, when n=1, these solutions constitute a generalization of that obtained by Yuen in [38]. Interestingly, numerical simulations show that the analytical solutions obtained can be used to describe the drifting phenomena of shallow water flows. In addition, the method proposed can be extended to other mathematical physics models such as higher-dimensional Hunter-Saxton equations and Degasperis-Procesi equations.

Submitted March 28, 2016. Published February 16, 2017.
Math Subject Classifications: 35C06, 35C05, 35Q35, 76N10
Key Words: Camassa-Holm equation; elliptic symmetry; multi-dimensional Camassa-Holm-type system; perturbational solutions

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Hongli An
College of Sciences
Nanjing Agricultural University
Nanjing 210095, China
email: kaixinguoan@163.com
Mankam Kwong
Department of Applied Mathematics
The Hong Kong Polytechnic University
Hung Hom, Kowloon, Hong Kong
email: mankam.kwong@polyu.edu.hk
Manwai Yuen
Department of Mathematics and Information Technology
The Education University of HongKong
10 Lo Ping Road Road, Tai Po
New Territories, Hong Kong
email: nevetsyuen@hotmail.com

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