A multiple Riccati equations rational expansion method and novel solutions of the Broer–Kaup–Kupershmidt system

To construct exact solutions of nonlinear partial differential equation, a multiple Riccati equations rational expansion method (MRERE) is presented and a series of novel solutions of the Broer–Kaup–Kupershmidt system are found. The novel solutions obtained by MRERE method include solutions of hyperbolic (solitary) function and triangular periodic functions appearing at the same time.

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

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

[3]  Li Biao,et al.  Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation , 2003 .

[4]  Yong Chen,et al.  Auto-Bäcklund transformation and exact solutions for modified nonlinear dispersive mK(m,n) equations , 2003 .

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

[6]  Yong Chen,et al.  A New Riccati Equation Rational Expansion Method and Its Application , 2005 .

[7]  S. Lou,et al.  Abundant Coherent Structures of the (2+1)-dimensional Broer-Kaup-Kupershmidt Equation , 2001 .

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

[9]  M. Wadati,et al.  Relationships among Inverse Method, Bäcklund Transformation and an Infinite Number of Conservation Laws , 1975 .

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

[11]  Engui Fan,et al.  Soliton solutions for the new complex version of a coupled KdV equation and a coupled MKdV equation , 2001 .

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

[13]  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 .

[14]  Zhang Hong-qing,et al.  New Families of Rational Form Solitary Wave Solutions to (2+1)-Dimensional Broer Kaup Kupershmidt System , 2005 .

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

[16]  Yong Chen,et al.  Exact Solutions for a Family of Variable-Coefficient “Reaction–Duffing” Equations via the Bäcklund Transformation , 2002 .

[17]  M. Wadati,et al.  Simple Derivation of Bäcklund Transformation from Riccati Form of Inverse Method , 1975 .

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

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

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

[21]  Peter A. Clarkson,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering: Remarks on Riemann-Hilbert problems , 1991 .

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

[23]  Qi Wang,et al.  A new Jacobi elliptic function rational expansion method and its application to (1 + 1)-dimensional dispersive long wave equation , 2005 .

[24]  Qi Wang,et al.  A new Riccati equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation , 2005 .