Auto-Bcklund transformation and novel exact analytic solutions for generalized variable-coefficient BKP equation

Xiang-hua MENG; Rui-lin XU; Xiao-ge XU

doi:10.3969/j.issn.1007-5461.2014.06.004

[1] Gardner C S, Greene J M, Kruskal M D, et al. Method for solving the Korteweg-de Vries equation ［J］. Phys. Rev. Lett., 1967, 19: 1095-1097.

[2] Ablowitz M J, Segur H. Solitons and the Inverse Scattering Transformation ［M］. Philadelphia SIAM, PA, 1981.

[3] Matsuno Y. Bilinear Transformation Method ［M］. London: Academic Press Inc., 1984.

[4] Rogers C, Schief W K. Bcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory ［M］. Cambridge: Cambridge University Press, 2002.

[6] Wang X, Chen Y. Darboux transformations and N-soliton solutions of two (2+1)-dimensional nonlinear equations ［J］. Communications in Theoretical Physics, 2014, 61: 423-430.

[7] Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons ［J］. Phys. Rev. Lett., 1971, 27: 1192-1194.

[8] Hirota R. The Direct Method in Soliton Theory ［M］. Cambridge: Cambridge University Press, 2004.

[9] Hu X B, Wang H Y. New type of Kadomtsev-Petviashvili equation with self-consistent sources and its bilinear Bcklund transformation ［J］. Inverse Problems, 2007, 23: 1433-1444.

[10] Xu X G, Meng X H. Integrable properties for a generalized non-isospectral and variable-coefficient Korteweg-de Veris model ［J］. Mod. Phys. Lett. B, 2010, 24: 1023-1032.

[11] Wang M L, Zhou Y B. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics ［J］. Phys. Lett. A, 1996, 216: 67-75.

[13] Liang Y Q, Wei G M, Li X N. New variable separation solutions and nonlinear phenomena for the (2+1)- dimensional modified Korteweg-de Vries equation ［J］. Communications in Nonlinear Science and Numerical Simulation, 2011, 16: 603-609.

[14] Xu G Q. A note on the Painleve test for the nonlinear variable-coefficient PDEs ［J］. Computer Physics Communications, 2009, 180: 1137-1144.

[15] Wei G M, Gao Y T, Meng X H, et al. Painleve property and new analytic solutions for a variable- coefficient Kadomtsev-Petviashvili equation with symbolic computation ［J］. Chin. Phys. Lett., 2008, 25: 1599-1602.

[18] Wazwaz A M. Multiple-front solutions for the Burgers-Kadomtsev-Petviashvili equation ［J］. Applied Mathematics and Computation, 2008, 200: 437-443.

[19] Taghizadeh N, Mirzazadeh M, Farahrooz F. Exact solutions of the modified KdV-KP equation and the Burgers-KP equation by using the first integral method ［J］. Applied Mathematical Modelling, 2011, 35: 3991-3997.