New travelling wave solutions of the generalized coupled Hirota–Satsuma KdV system

Abstract In this paper, by the application of hyperbolic function, triangle function and symbolic computation, we devise a new method to seek the exact travelling wave solutions of the nonlinear partial differential equations in mathematical physics. The generalized coupled Hirota–Satsuma KdV system is chosen to illustrate the approach. As a consequence, abundant new solitary and periodic solutions are obtained.

[1]  Yan Zhen-Ya,et al.  New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota Satsuma KdV System , 2002 .

[2]  Yong Chen,et al.  Explicit exact solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order , 2003 .

[3]  Wenxiu Ma,et al.  The Hirota-Satsuma Coupled KdV Equation and a Coupled Ito System Revisited , 2000 .

[4]  Hong-qing Zhang,et al.  Soliton-like and period form solutions for high dimensional nonlinear evolution equations , 2003 .

[5]  J. Weiss,et al.  The sine‐Gordon equations: Complete and partial integrability , 1984 .

[6]  Bo Tian,et al.  Generalized tanh method with symbolic computation and generalized shallow water wave equation , 1997 .

[7]  Y. C. Hon,et al.  A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves , 2003 .

[8]  Bo Tian,et al.  Some two-dimensional and non-travelling-wave observable effects of the shallow-water waves , 2002 .

[9]  Q. P. Liu,et al.  New Darboux transformation for Hirota–Satsuma coupled KdV system , 2002 .

[10]  Zhenya Yan,et al.  Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres , 2003 .

[11]  Zhenya Yan,et al.  The extended Jacobian elliptic function expansion method and its application in the generalized Hirota–Satsuma coupled KdV system , 2003 .

[12]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[13]  Willy Hereman,et al.  Exact solitary wave solutions of coupled nonlinear evolution equations using MACSYMA , 1991 .

[14]  Yong Chen,et al.  Exact solutions for a new class of nonlinear evolution equations with nonlinear term of any order , 2003 .

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

[16]  H. Tam,et al.  Two Integrable Coupled Nonlinear Systems , 1999 .

[17]  Robert Conte,et al.  Link between solitary waves and projective Riccati equations , 1992 .

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

[19]  Zhenya Yan,et al.  Explicit and exact traveling wave solutions of Whitham–Broer–Kaup shallow water equations , 2001 .

[20]  M. Wadati,et al.  Wave Propagation in Nonlinear Lattice. III , 1975 .