Perturbational self-similar solutions for multi-dimensional camassa-holm-type equations

Hongli AN, Man Kam KWONG, Man Wai YUEN

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1 Citation (Scopus)

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.
Copyright © 2017 Texas State University.
Original languageEnglish
Pages (from-to)1-12
JournalElectronic Journal of Differential Equations
Volume2017
Issue number48
Publication statusPublished - 2017

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Self-similar Solutions
Degasperis-Procesi Equation
Shallow Water Flow
Characteristics Method
Type Systems
Analytical Solution
High-dimensional
Physics
Symmetry
Numerical Simulation
Model
Generalization
Class

Citation

An, H., Kwong, M., & Yuen, M. (2017). Perturbational self-similar solutions for multi-dimensional camassa-holm-type equations. Electronic Journal of Differential Equations, 2017(48), 1–12.

Keywords

  • Camassa-Holm equation
  • Elliptic symmetry
  • Multi-dimensional Camassa-Holm-type system
  • Perturbational solutions