The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term

By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg–de Vries (KdV) equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.

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

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

[3]  P. Hoodbhoy.  POLARIZED DEEP INELASTIC SCATTERING FROM THE CLOUDY BAG MODEL. A FAILURE , 1986 .

[4]  E. J. Parkes,et al.  Travelling solitary wave solutions to a seventh-order generalized KdV equation , 1996 .

[5]  K. Fujikawa,et al.  BRS anomaly and the weyl freedom in string theory , 1988 .

[6]  Mingliang Wang,et al.  A new Bäcklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients , 2001 .

[7]  Zuo-nong Zhu,et al.  Painlevé property, Bäcklund transformation, Lax pair and soliton-like solution for a variable coefficient KP equation , 1993 .

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

[9]  Sun Jiong,et al.  Auxiliary equation method for solving nonlinear partial differential equations , 2003 .

[10]  Zhang Jie-fang.  Bäcklund transformation and variable separation solutions for the generalized Nozhnik-Novikov-Veselov equation , 2002 .

[11]  Yan Zhen-Ya,et al.  New explicit exact solutions for a generalized Hirota-Satsuma coupled KdV system and a coupled MKdV equation , 2003 .

[12]  E. J. Parkes,et al.  Exact solutions to the two-dimensional Korteweg-de Vries-Burgers equation , 1994 .

[13]  Li Hua-mei.  New exact solutions of nonlinear Gross–Pitaevskii equation with weak bias magnetic and time-dependent laser fields , 2005 .

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

[15]  M. J. Vedan,et al.  Auto‐Bäcklund transformation, Lax pairs, and Painlevé property of a variable coefficient Korteweg–de Vries equation. I , 1986 .

[16]  Young-Dae Jung,et al.  Auto-Bäcklund transformation and analytic solutions for general variable-coefficient KdV equation , 1999 .

[17]  Zhang Wei-guo,et al.  Explicit exact solitary wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms , 2003 .

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

[19]  Yan Zhen-ya,et al.  EXACT SOLITON SOLUTIONS OF THE VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNTIONS , 1999 .

[20]  G. Manzoni,et al.  Headache classification: criticism and suggestions , 2004, Neurological Sciences.

[21]  Zuo-nong Zhu,et al.  Lax pair, Bäcklund transformation, solitary wave solution and finite conservation laws of the general KP equation and MKP equation with variable coefficients , 1993 .

[22]  Zhang Jie-Fang,et al.  TRUNCATED EXPANSION METHOD AND NEW EXACT SOLITON-LIKE SOLUTION OF THE GENERAL VARIABLE COEFFICIENT KdV EQUATION , 2001 .

[23]  L. Garrido,et al.  Subtle errors in αs determination using “corrected data” of energy-energy asymmetry , 1986 .

[24]  Mingliang Wang.  SOLITARY WAVE SOLUTIONS FOR VARIANT BOUSSINESQ EQUATIONS , 1995 .

[25]  Steeb,et al.  Kadomtsev-Petviashvili equation with explicit x and t dependence. , 1985, Physical review. A, General physics.