Traveling Wave Solutions of a Generalized Camassa-Holm Equation: A Dynamical System Approach
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-11-24
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
We investigate a generalized Camassa-Holm equation C(3,2,2): ut+kux+γ1uxxt+γ2(u3)x+γ3ux(u2)xx+γ3u(u2)xxx=0.
We show that the C(3,2,2) equation can be reduced to a planar polynomial differential system by transformation of variables.
We treat the planar polynomial differential system by the dynamical systems theory and present a phase space analysis of their singular points.
Two singular straight lines are found in the associated topological vector field.
Moreover, the peakon, peakon-like, cuspon, smooth soliton solutions of the generalized Camassa-Holm equation under inhomogeneous boundary condition are obtained.
The parametric conditions of existence of the single peak soliton solutions are given by using the phase portrait analytical technique.
Asymptotic analysis and numerical simulations are provided for single peak soliton, kink wave, and kink compacton solutions of the C(3,2,2) equation.
American Psychological Association (APA)
Zhang, Lina& Song, Tao. 2015. Traveling Wave Solutions of a Generalized Camassa-Holm Equation: A Dynamical System Approach. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-19.
https://search.emarefa.net/detail/BIM-1074275
Modern Language Association (MLA)
Zhang, Lina& Song, Tao. Traveling Wave Solutions of a Generalized Camassa-Holm Equation: A Dynamical System Approach. Mathematical Problems in Engineering No. 2015 (2015), pp.1-19.
https://search.emarefa.net/detail/BIM-1074275
American Medical Association (AMA)
Zhang, Lina& Song, Tao. Traveling Wave Solutions of a Generalized Camassa-Holm Equation: A Dynamical System Approach. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-19.
https://search.emarefa.net/detail/BIM-1074275
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074275