Soliton, kink and antikink solutions of a 2-component of the Degasperis-Procesi equation

Abstract In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the traveling wave solutions of a 2-component of the Degasperis–Procesi equation. The expressions for smooth soliton, kink and antikink solutions are obtained.

[1]  Hans Lundmark,et al.  Multi-peakon solutions of the Degasperis–Procesi equation , 2003, nlin/0503033.

[2]  Ji-Huan He,et al.  Construction of solitary solution and compacton-like solution by variational iteration method , 2006 .

[3]  Z. Qiao.  M-Shape peakons, dehisced solitons, cuspons and new 1-peak solitons for the Degasperis–Procesi equation , 2008 .

[4]  Yoshimasa Matsuno,et al.  Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit , 2005 .

[5]  Yoshimasa Matsuno,et al.  Cusp and loop soliton solutions of short-wave models for the Camassa–Holm and Degasperis–Procesi equations , 2006 .

[6]  Luo Dingjun,et al.  Bifurcation Theory and Methods of Dynamical Systems , 1998 .

[7]  Anjan Biswas,et al.  1-soliton solution of the K(m,n) equation with generalized evolution , 2008 .

[8]  E. J. Parkes,et al.  Periodic and solitary-wave solutions of the Degasperis-Procesi equation , 2004 .

[9]  Min-ying Tang,et al.  A new type of bounded waves for Degasperis–Procesi equation , 2006 .

[10]  Abdul-Majid Wazwaz,et al.  Compact and noncompact structures for a variant of KdV equation in higher dimensions , 2002, Appl. Math. Comput..

[11]  Yoshimasa Matsuno,et al.  The N-soliton solution of the Degasperis–Procesi equation , 2005, nlin/0511029.

[12]  Jianwei Shen,et al.  Bifurcations of smooth and non-smooth travelling wave solutions in the generalized Camassa–Holm equation , 2005 .

[13]  F. Rybicki,et al.  COULOMB FUNCTIONS FOR COMPLEX ENERGIES. , 1984 .

[14]  Lixin Tian,et al.  Soliton solution of the osmosis K(2,2)K(2,2) equation , 2008, 0907.5522.

[15]  Antonio Degasperis,et al.  Symmetry and perturbation theory , 1999 .

[16]  Yi Zhang,et al.  Exact loop solutions, cusp solutions, solitary wave solutions and periodic wave solutions for the special CH–DP equation , 2009 .

[17]  Allen Parker,et al.  Cusped solitons of the Camassa-Holm equation. I. Cuspon solitary wave and antipeakon limit , 2007 .

[18]  Hans Lundmark,et al.  Formation and Dynamics of Shock Waves in the Degasperis-Procesi Equation , 2007, J. Nonlinear Sci..

[19]  Darryl D. Holm,et al.  A New Integrable Equation with Peakon Solutions , 2002, nlin/0205023.

[20]  Lixin Tian,et al.  Solitons, peakons and periodic cusp wave solutions for the Fornberg-Whitham equation , 2010 .

[21]  Zheng-rong Liu,et al.  A note on solitary waves for modified forms of Camassa–Holm and Degasperis–Procesi equations , 2007 .

[22]  Jonatan Lenells,et al.  Traveling wave solutions of the Degasperis-Procesi equation , 2005 .

[23]  L. Tian,et al.  The bifurcation and peakon for Degasperis–Procesi equation , 2006 .

[24]  Zhenya Yan,et al.  Modified nonlinearly dispersive mK(m,n,k) equations: I. New compacton solutions and solitary pattern solutions , 2003 .