Multiple Soliton Solutions for a New Generalization of the Associated Camassa-Holm Equation by Exp-Function Method

Dissipative Solutions for the Camassa–holm Equation

has been extensively studied since the first systematic analysis in [5, 6]. Part of the attraction is the surprising complexity of the equation and its deep and nontrivial properties. To list a few of its peculiarities: The Camassa–Holm equation has a bi-Hamiltonian structure [16], it is completely integrable [5], and it has infinitely many conserved quantities [5]. Here we study the equation w...

Decomposition Method for Camassa-holm Equation

A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions

An explicit reciprocal transformation between a 2-component generalization of the CamassaHolm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established, this transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH sys...

Elastic collisions among peakon solutions for the Camassa–Holm equation

The purpose of this paper is to study the dynamics of the interaction among a special class of solutions of the one-dimensional Camassa-Holm equation. The equation yields soliton solutions whose identity is preserved through nonlinear interactions. These solutions are characterized by a discontinuity at the peak in the wave shape and are thus called peakon solutions. We apply a particle method ...

A self-adaptive mesh method for the Camassa-Holm equation

A self-adaptive mesh method is proposed for the numerical simulations of the Camassa-Holm equation based on its integrable semi-discretization. It is an integrable scheme, possessing the N-soliton solution (see J. Phys. A, 41 355205). Moreover, it is called a self-adaptive mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is...