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Periodic Loop Solutions of the CH-DP Equation
Periodic loop solutions of the CH-DP equation are investigated by using the dynamical system theory. The solutions are characterized by two parameters. The periodic loops existent conditions are found. Explicit analytical periodic loop solutions of CH-DP equation are derived.
Keywords
Cammasa-holm Equation, CH-DP Equation, Traveling Wave System, Singular Point, Periodic Loops
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- Camassa R and Holm DD (1993) An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71(11), 1661-1664.
- Degasperis A and Procesi M (1999) Asymptotic integrability. In: Symmetry and Perturbation Theory. Degasperis A and Aeta GG (Eds.), World Scientific, Singapore. pp: 23-27.
- Degasperis A, Holm DD and Hone ANW (2002) A new integrable equation with peakon solutions. Theoret. Math. Phys. 133, 1463-1474.
- Holm DD and Staley MF (2003) Nonlinear balance and exchange of stability in dynamics of solitons, peakons/cliffs and leftons in a 1+1 nonlinear evolutionary PDE. Phys. Lett. 308437-308444.
- Holm DD and Staley MF (2003) Wave structure and nonlinear balances in a family of evolutionary PDEs. SIAM. J.Appl. Dyn. Syst. 2, 323-380.
- Dullin HR, Gottwald GA and Holm DD (2004) On asymptotically equivalent shallow water wave equations. Phys. 190, 1-14.
- Liu ZR and Ouyang ZY (2007) Anote on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equation. Phys. Lett. 366, 377-381.
- Vakhnenko O and Parkes J (2004) The Connection of the Degasperis–Procesi Equation with the Vakhnenko Equation. Proc. Instt. of Maths. of NAS of Ukraine. 50(1), 493–497.
- Li JB and Yi Z (2009) Exac loop solutions, cusp solutions, solitary wave solutions and periodic wave solutions for CH-DP equation. Nonlinear Anal. Real World Appl. 10(4), 2502-2507.
- Xie SL and Wang L (2010) Compacton and generalized kink wave solutions of the CH–DP equation. Appl. Math. Comput. 215, 4028–4039.
- Byrd PF and Friedman MD (1971) Handbook of elliptic integrals for engineers and scientists. Berlin, Springer.
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