Back to Search
Start Over
Orbital stability and dynamical behaviors of solitary waves for the Camassa–Holm equation with quartic nonlinearity
- Source :
- Chaos, Solitons & Fractals. 76:40-46
- Publication Year :
- 2015
- Publisher :
- Elsevier BV, 2015.
-
Abstract
- In this paper we prove that the Camassa–Holm equation with quartic nonlinearity is non-integrable via the Painleve method. The orbital stability of solitary waves for this equation is investigated by constructing a functional extremum problem. This result demonstrates that the resulting solitary wave is unstable when its speed lies in the narrow region of the critical value that connects with the bifurcation condition. In contrast when the speed surpasses the narrow region, the solitary wave is stable. In addition, the stable solitary wave turns into a chaotic state when is driven externally. If a damping term controller is added to the perturbed equation, the solitary wave can also propagate stably under a certain condition. Finally our numerical results show that the perturbed equation is not well controlled when a certain resonant-frequency occurs and is well controlled with a smaller wave speed as well as a higher nonlinear convection.
- Subjects :
- Camassa–Holm equation
General Mathematics
Applied Mathematics
Mathematical analysis
Chaotic
General Physics and Astronomy
Statistical and Nonlinear Physics
State (functional analysis)
Critical value
Nonlinear system
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Classical mechanics
Control theory
Quartic function
Nonlinear Sciences::Pattern Formation and Solitons
Bifurcation
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 76
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........603f4e282e486e086886f99ba8cb06b4