New Families of Rational Form Solitary Wave Solutions to (2+1)-Dimensional Broer Kaup Kupershmidt System

Taking the (2+1)-dimensional Broer–Kaup–Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.

[1]  J. Rogers Chaos , 1876, Molecular Vibrations.

[2]  Vladimir E. Zakharov,et al.  Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .

[3]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[4]  M. Boiti,et al.  Spectral transform for a two spatial dimension extension of the dispersive long wave equation , 1987 .

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

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

[7]  E. J. Parkes,et al.  Travelling solitary wave solutions to a compound KdV-Burgers equation , 1997 .

[8]  S. Lou,et al.  Infinitely many Lax pairs and symmetry constraints of the KP equation , 1997 .

[9]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[10]  Andrew G. Glen,et al.  APPL , 2001 .

[11]  Zhenya Yan,et al.  New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water , 2001 .

[12]  J. van Leeuwen,et al.  Algorithms and Computation , 2002, Lecture Notes in Computer Science.

[13]  Li Yi-Shen,et al.  The Exact Solutions of Some (2+1)-Dimensional Integrable Systems , 2002 .

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

[15]  En-Gui Fan,et al.  Traveling wave solutions for nonlinear equations using symbolic computation , 2002 .

[16]  S. Lou (2 + 1)-dimensional compacton solutions with and without completely elastic interaction properties , 2002 .

[17]  Yong Chen,et al.  Explicit exact solutions for new general two-dimensional KdV-type and two-dimensional KdV–Burgers-type equations with nonlinear terms of any order , 2002 .

[18]  S. Lou,et al.  Extended multilinear variable separation approach and multivalued localized excitations for some (2+1)-dimensional integrable systems , 2003 .

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

[20]  Zhenya Yan The new extended Jacobian elliptic function expansion algorithm and its applications in nonlinear mathematical physics equations , 2003 .

[21]  Tang Chen,et al.  New Predictor-Corrector Methods Based on Exponential Time Differencing for Systems of Nonlinear Differential Equations , 2004 .

[22]  Zhang Hong-qing,et al.  New Exact Travelling Wave Solutions to Hirota Equation and (1+1)-Dimensional Dispersive Long Wave Equation* , 2004 .

[23]  Yong Chen,et al.  General projective Riccati equation method and exact solutions for generalized KdV-type and KdV–Burgers-type equations with nonlinear terms of any order , 2004 .