Bäcklund transformation and multi-soliton solutions for a (2 + 1)-dimensional Korteweg-de Vries system via symbolic computation

[1]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[2]  G. Lamb Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium , 1971 .

[3]  R. Hirota Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[4]  A. Scott,et al.  The soliton: A new concept in applied science , 1973 .

[5]  M. Wadati,et al.  Bäcklund Transformation for the Exponential Lattice , 1975 .

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

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

[8]  R. Hirota,et al.  N-Soliton Solutions of Model Equations for Shallow Water Waves , 1976 .

[9]  R. Hirota,et al.  Nonlinear Evolution Equations Generated from the Bäcklund Transformation for the Boussinesq Equation , 1977 .

[10]  P. Clarkson,et al.  Painleve analysis of the non-linear Schrodinger family of equations , 1987 .

[11]  V. Dubrovsky,et al.  delta -dressing and exact solutions for the (2+1)-dimensional Harry Dym equation , 1994 .

[12]  R. Radha,et al.  Singularity analysis and localized coherent structures in (2+1)‐dimensional generalized Korteweg–de Vries equations , 1994 .

[13]  S. Lou Generalized dromion solutions of the (2+1)-dimensional KdV equation , 1995 .

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

[15]  S. Lou Abundant solitary wave structures of the nonlinear coupled scalar field equations , 1999 .

[16]  Yi Zhang,et al.  A modified Bäcklund transformation and multi-soliton solution for the Boussinesq equation , 2004 .

[17]  M. P. Barnett,et al.  Symbolic calculation in chemistry: Selected examples , 2004 .

[18]  Shu-fang Deng,et al.  The Bäcklund transformation and novel solutions for the Toda lattice , 2005 .

[19]  Shu-fang Deng Bäcklund transformation and soliton solutions for KP equation , 2005 .

[20]  Zhenyun Qin,et al.  Darboux and Bäcklund transformations for the nonisospectral KP equation , 2006 .

[21]  Ai-Hua Chen,et al.  Darboux transformation and soliton solutions for Boussinesq–Burgers equation , 2006 .

[22]  C. Zheng,et al.  Chaos, solitons and fractals in (2 + 1)-dimensional KdV system derived from a periodic wave solution , 2007 .

[23]  Xing Lü,et al.  Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications , 2007 .

[24]  B. Tian,et al.  Symbolic computation on cylindrical-modified dust-ion-acoustic nebulons in dusty plasmas , 2007 .

[25]  Tao Xu,et al.  Lax pair, Bäcklund transformation and N-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation , 2007 .

[26]  B. Tian,et al.  Bäcklund transformation in bilinear form for a higher-order nonlinear Schrödinger equation , 2008 .

[27]  Tao Geng,et al.  A new application of Riccati equation to some nonlinear evolution equations , 2008 .

[28]  Xiang-Hua Meng,et al.  Multi-soliton solutions and a Bäcklund transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation with symbolic computation , 2008 .