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Waves in Random and Complex Media Volume 21, 2011 - Issue 4
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Original Articles

Soliton and shock wave solutions to the Degasperis–Procesi equation with power law nonlinearity

Houria Triki Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, PO Box 12, 2300 Annaba, Algeria
,
T. Hayat Department of Mathematics, Qaid-i-Azam University, Islamabad-44000, Pakistan; Department of Physics, King Saud University, P.O. Box 2455, Riyadh-11451, Saudi Arabia
,
Omar M. Aldossary Department of Physics, King Saud University, P.O. Box 2455, Riyadh-11451, Saudi Arabia
&
Anjan Biswas Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USACorrespondence[email protected]
Pages 543-553 | Received 30 Mar 2011, Accepted 05 Jun 2011, Published online: 04 Aug 2011

References

  • Biswas , A , Konar , S and Zerrad , E . 2007 . Soliton perturbation theory for the general modified Degasperis–Procesi and Camassa–Holm equation . Int. J. Mod. Math. , 2 : 35 – 40 .
  • Fan , X , Yang , S , Yin , J and Tian , L . 2011 . Peakon, loop and solitary travelling wave solutions for the generalized modified CH-DP equation . Appl. Math. Comput. , 217 : 4812 – 4818 .
  • Guha , P . 2007 . Euler–Poincaré formalism of (two component) Degasperis–Procesi and Holm–Staley type systems . J. Nonlinear Math. Phys. , 14 : 390 – 421 .
  • He , B , Rui , W , Li , S and Chen , C . 2008 . Bounded travelling wave solutions for a modified form of generalized Degasperis–Procesi equation . Appl. Math. Comput. , 206 : 113 – 123 .
  • Li , J and Liu , Z . 2000 . Smooth and non-smooth traveling waves in a randomly dispersive equation . Appl. Math. Model. , 25 : 41 – 56 .
  • Shen , J and Xu , W . 2006 . Smooth and non-smooth travelling wave solutions of a generalized Degasperis–Procesi equation . Appl. Math. Comput. , 182 : 1418 – 1429 .
  • Wazwaz , A-W . 2007 . New solitary wave solutions to the modified forms of the Degasperis–Procesi and Camassa-Holm equation . Appl. Math. Comput. , 186 : 130 – 141 .
  • Xie , S , Lin , Q and Gao , B . 2011 . Periodic and solitary traveling wave solutions of a CH-DP equation . Comm. Nonlinear Sci. Numer. Simul. , 16 : 3941 – 3948 .
  • Yu , L , Tian , L and Wang , X . 2006 . The bifurcation and peakon for the Degasperis–Procesi equation . Chaos, Solitons Fractals , 30 : 956 – 966 .
  • Zhou , J and Tian , L . 2009 . Solitons, peakons, and periodic cuspons of a generalized Degasperis–Procesi equation . Math. Problems Eng. , 2009 249361

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