Travelling wave solutions for a class of nonlinear fourth order variant of a generalized Camassa-Holm equation

In this paper, we study a class of nonlinear fourth order analogue of a generalized Camassa-Holm equation by using sine-cosine method. It is shown that this class gives compactons and solitary patterns solutions.

[1]  Wentao Huang,et al.  Bifurcations of travelling wave solutions for the generalized double sinh-Gordon equation , 2007, Appl. Math. Comput..

[2]  E. Fan,et al.  Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics , 2003 .

[3]  P. Olver.  Applications of Lie Groups to Differential Equations , 1986 .

[4]  Abdul-Majid Wazwaz,et al.  Solutions of compact and noncompact structures for nonlinear Klein-Gordon-type equation , 2003, Appl. Math. Comput..

[5]  Sheng Zhang.  New exact solutions of the KdV–Burgers–Kuramoto equation , 2006 .

[6]  Abdul-Majid Wazwaz,et al.  A reliable treatment of the physical structure for the nonlinear equation K(m, n) , 2005, Appl. Math. Comput..

[7]  E. Fan,et al.  Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation , 2001 .

[8]  L. Tian,et al.  New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa–Holm equations , 2004 .

[9]  P. Clarkson,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering: References , 1991 .

[10]  R. Hirota,et al.  Soliton solutions of a coupled Korteweg-de Vries equation , 1981 .

[11]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[12]  Abdul-Majid Wazwaz,et al.  A sine-cosine method for handlingnonlinear wave equations , 2004, Math. Comput. Model..

[13]  Mingliang Wang.  Exact solutions for a compound KdV-Burgers equation , 1996 .

[14]  Zhenya Yan.  New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations , 2001 .

[15]  Hong-qing Zhang,et al.  New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics , 1999 .

[16]  Abdul-Majid Wazwaz,et al.  Analytic study on nonlinear variants of the RLW and the PHI-four equations , 2007 .

[17]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .

[18]  S. Lai,et al.  Peakons, solitary patterns and periodic solutions for generalized Camassa–Holm equations , 2008 .

[19]  Jibin Li,et al.  TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS , 2002 .

[20]  Abdul-Majid Wazwaz,et al.  Solitons and periodic solutions for the fifth-order KdV equation , 2006, Appl. Math. Lett..

[21]  G. Bluman,et al.  Symmetries and differential equations , 1989 .

[22]  Abdul-Majid Wazwaz,et al.  A class of nonlinear fourth order variant of a generalized Camassa-Holm equation with compact and noncompact solutions , 2005, Appl. Math. Comput..

[23]  P. Clarkson,et al.  Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations , 1999, math/9901154.