Quasi-periodic wave solutions for the (2+1) -dimensional generalized Calogero–Bogoyavlenskii–Schiff (CBS) equation

Abstract The Hirota bilinear method is implemented to directly construct quasi-periodic wave solutions in terms of theta functions for a Hirota bilinear equation. The result is applied to the (2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff (CBS) equation, thereby yielding their quasi-periodic wave solutions under the Backlund transformation u = η y + 3 δ [ l n f ( x , y , t ) ] x .

[1]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions of two extended model equations for shallow water waves , 2008, Appl. Math. Comput..

[2]  C Cao,et al.  NONLINEARIZATION OF THE LAX SYSTEM FOR AKNS HIERARCHY , 1990 .

[3]  Engui Fan,et al.  Quasi-periodic waves and an asymptotic property for the asymmetrical Nizhnik–Novikov–Veselov equation , 2009 .

[4]  Wenxiu Ma,et al.  A second Wronskian formulation of the Boussinesq equation , 2009 .

[5]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[6]  Abdul-Majid Wazwaz,et al.  The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves , 2008, Appl. Math. Comput..

[7]  Ryogo Hirota,et al.  A New Form of Bäcklund Transformations and Its Relation to the Inverse Scattering Problem , 1974 .

[8]  Xianguo Geng,et al.  Quasi-periodic solutions for some 2+1-dimensional discrete models , 2003 .

[9]  H. Dai,et al.  Decomposition of a 2 + 1-dimensional Volterra type lattice and its quasi-periodic solutions , 2003 .

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

[11]  Yong Chen,et al.  Exact Analytical Solutions of the Generalized Calogero-Bogoyavlenskii-Schiff Equation Using Symbolic Computation , 2004 .

[12]  Chen Yong,et al.  Infinitely many symmetries and symmetry reduction of (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation , 2009 .

[13]  Kwok Wing Chow,et al.  A class of exact, periodic solutions of nonlinear envelope equations , 1995 .

[14]  An integrable lattice equation related to the nKN system , 2010 .

[15]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[16]  Yunbo Zeng,et al.  Binary constrained flows and separation of variables for soliton equations , 2001, The ANZIAM Journal.

[17]  Engui Fan,et al.  Quasiperiodic waves and asymptotic behavior for Bogoyavlenskii's breaking soliton equation in (2+1) dimensions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  K. Chow Superposition of solitons and discrete evolution equations , 1994 .

[19]  Wen-Xiu Ma,et al.  Wronskian solutions of the Boussinesq equation—solitons, negatons, positons and complexitons , 2007 .

[20]  Akira Nakamura,et al.  A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. : II. Exact One- and Two-Periodic Wave Solution of the Coupled Bilinear Equations , 1980 .

[21]  Xianguo Geng,et al.  Relation between the Kadometsev–Petviashvili equation and the confocal involutive system , 1999 .

[22]  Wen-Xiu Ma,et al.  An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems , 1994 .

[23]  C. Rogers,et al.  Bäcklund and Darboux transformations : the geometry of solitons : AARMS-CRM Workshop, June 4-9, 1999, Halifax, N.S., Canada , 2001 .

[24]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for the Lax-Kadomtsev-Petviashvili (Lax-KP) equation , 2008, Appl. Math. Comput..

[25]  X. Geng,et al.  Explicit solutions of some (2 + 1)-dimensional differential-difference equations , 2003 .

[26]  Xing-Biao Hu,et al.  An integrable symmetric (2+1)-dimensional Lotka–Volterra equation and a family of its solutions , 2005 .

[27]  Wen-Xiu Ma,et al.  Complexiton solutions of the Toda lattice equation , 2004 .

[28]  Y. Hon,et al.  A KIND OF EXPLICIT QUASI-PERIODIC SOLUTION AND ITS LIMIT FOR THE TODA LATTICE EQUATION , 2008 .

[29]  Kwok Wing Chow Periodic solutions for a system of four coupled nonlinear Schrödinger equations , 2001 .

[30]  Chunxia Li,et al.  Pfaffianization of the differential-difference KP equation , 2004 .

[31]  Xing-Biao Hu,et al.  A vector potential KdV equation and vector Ito equation: soliton solutions, bilinear Bäcklund transformations and Lax pairs , 2003 .

[32]  K. Chow A class of doubly periodic waves for nonlinear evolution equations , 2002 .

[33]  Akira Nakamura,et al.  A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution , 1979 .

[34]  Wen-Xiu Ma,et al.  Complexiton solutions to the Korteweg–de Vries equation , 2002 .

[35]  Wen-Xiu Ma,et al.  EXACT ONE-PERIODIC AND TWO-PERIODIC WAVE SOLUTIONS TO HIROTA BILINEAR EQUATIONS IN (2+1) DIMENSIONS , 2008, 0812.4316.

[36]  D. P. Novikov,et al.  Algebraic-geometric solutions of the Harry Dym equation , 1999 .

[37]  Xianguo Geng,et al.  Algebro-geometric solution of the 2+1 dimensional Burgers equation with a discrete variable , 2002 .

[38]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[39]  D. F. Lawden Elliptic Functions and Applications , 1989 .