Hongli An, Mankam Kwong, Manwai Yuen
Abstract:
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 |
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Mankam Kwong Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong email: mankam.kwong@polyu.edu.hk |
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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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