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COEXISTENCE OF MULTIFARIOUS EXPLICIT NONLINEAR WAVE SOLUTIONS FOR MODIFIED FORMS OF CAMASSA–HOLM AND DEGAPERIS–PROCESI EQUATIONS.
- Source :
-
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering . Jul2009, Vol. 19 Issue 7, p2267-2282. 16p. 7 Diagrams. - Publication Year :
- 2009
-
Abstract
- In this paper, we consider two nonlinear equations ut - uxxt + 3u2ux = 2uxuxx + uuxxx and ut - uxxt + 4u2ux = 3uxuxx + uuxxx which are called modified forms of Camassa–Holm and Degaperis–Procesi equations, respectively. For given constant wave speed, we investigate the coexistence of multifarious explicit nonlinear wave solutions, solitary wave solution, peakon wave solution, singular wave solution, smooth periodic wave solution and singular periodic wave solution. Not only is the coexistence shown, but the concrete expressions are presented via the bifurcation method of dynamical systems. From our work it can be seen that these two equations possess a lot of similar properties, and the types of their explicit nonlinear wave solutions are more than that of Camassa–Holm and Degaperis–Procesi equations. Many previous results are our special cases. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONLINEAR waves
*EQUATIONS
*SOLITONS
*ELLIPTIC functions
*EXPONENTIAL functions
Subjects
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 19
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 44840090
- Full Text :
- https://doi.org/10.1142/S0218127409024050