The analytic expressions of peaked solitary wave solutions and peaked periodic wave solutions of Camassa-Holm equation are obtained by using bifurcation method of planar dynamical systems. The convergence of the peaked periodic wave solutions is proved. Numerical simulation results show the consiste
New peaked solitary wave solutions of the generalized Camassa–Holm equation
✍ Scribed by Lixin Tian; Xiuying Song
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 805 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0960-0779
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper, we consider generalized Camassa-Holm equations and the generalized weakly dissipative Camassa-Holm equations and derive some new exact peaked solitary wave solutions. For m ¼ 3, where m is representative of the strength of the nonlinearity, we give two types new exact traveling wave solutions of the generalized weakly dissipative Camassa-Holm equations.
📜 SIMILAR VOLUMES
The generalized magma equation, in which dispersion and nonlinearity are coupled together in a manner reminiscent of the Harry-Dym equation, is solved to indicate both periodic and aperiodic implicit solitary wave solutions. It is argued that the presence of an additional spatial derivative in the m
An exact 1-soliton solution of the generalized Camassa-Holm Kadomtsev-Petviashvili equation is obtained in this paper by the solitary wave ansatze. This solution is a generalized form of the solution that is obtained in earlier works.
In this letter we discuss the 2 q 1 -dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a pertu