Perturbational self-similar solutions for multi-dimensional Camassa-Holm-type equations
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Date
2017-02-16
Authors
An, Hongli
Kwong, Mankam
Yuen, Manwai
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Camassa-Holm equation, Elliptic symmetry, Multi-dimensional Camassa-Holm-type system, Perturbational solutions
Citation
An, H., Kwong, M., & Yuen, M. (2017). Perturbational self-similar solutions for multi-dimensional Camassa-Holm-type equations. <i>Electronic Journal of Differential Equations, 2017</i>(48), pp. 1-12.
Rights
Attribution 4.0 International