NEW EXACT SOLUTIONS FOR THE BOITI-LEON-PEMPINELLI EQUATIONS

Du Xianyun (P. R. China), Liu Xiqiang (P. R. China) and Zhengde Dai (P. R. China)

Received October 15, 2007

References:

[1] M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, PA, 1981. [2] R. Beals and R. R. Coifman, Scattering and inverse scattering for first order systems, Comm. Pure Appl. Math. 37 (1984), 39-90. [3] Z. Dai, S. Li, Q. Dai and J. Huang, Singular periodic soliton solutions and resonance for the Kadomtsev-Petviashvili equation, Chaos Solitons Fractals 34 (2007), 1148-1153. [4] Z. Dai, Z. Li, Z. Liu and D. Li, Exact cross kink-wave solutions and resonance for the Jimbo-Miwa equation, Phys. A 384 (2007), 285-290. [5] C. H. Gu, H. S. Hu and Z. X. Zhou, Darboux Transformations in Soliton Theory and its Geometric Applications, Shanghai Scientific and Technical Publishers, Shanghai, 1999. [6] W. Hereman, Exact solitary wave solutions of coupled nonlinear evolution equations using Macsyma, Comput. Phys. Comm. 65 (1996), 143-150. [7] R. Hirota and J. Satsuma, Soliton solutions of a coupled Korteweg-de Vries equation, Phys. Lett. A 85 (1981), 407-408. [8] S. B. Leble and N. V. Ustinov, Darboux transformations, deep reductions and solitons, J. Phys. A 26 (1993), 5007-5016. [9] De-Sheng Li and Hong-Qing Zhang, A new extend tanh-function method and its application to the dispersive long wave equation in (2 + 1) dimensions, Appl. Math. Comput. 147 (2004), 789-797. [10] X. Q. Liu and S. Jiang, New solutions of the 3+1 dimensional Jimbo-Miwa equation, Appl. Math. Comput. 158 (2004), 177-184. [11] X. Q. Liu and S. Jiang, Exact solutions of multi-component nonlinear Schrödinger and Klein-Gordon equations, Appl. Math. Comput. 160 (2005), 857-880. [12] Zhuosheng Lu and Hongqing Zhang, Soliton like and multi-soliton like solutions for the Boiti-Leon-Pempinelli equation, Chaos Solitons Fractals 19 (2004), 527-531. [13] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Amer. J. Phys. 60 (1992), 650-654. [14] W. Malfliet and W. Hereman, The tanh method: I, exact solutions of nonlinear evolution and wave equations, Phys. Scripta 56 (1996), 563-568. [15] V. B. Matveev and M. A. Salle, Darboux Transformation and Solitons, Springer, Berlin, 1991. [16] J. Satsuma and R. Hirota, A coupled KdV equation is one case of the four-reduction of the KP hierarchy, J. Phys. Soc. Japan 51 (1982), 3390-3397. [17] M. L. Wang, Solitary wave solutions for variant Boussinesq equations, Phys. Lett. A 199 (1995), 169-172. [18] M. L. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A 213 (1996), 279-287. [19] C. L. Zheng, J. P. Fang and L. Q. Chen, Bell-like and peak-like loop solitons in (2 + 1)-dimensional Boiti-Leon-Pempinelli system, Acta Phys. Sinica 54 (2005), 1468-1475.

Keywords and phrases: Boiti-Leon-Pempinelli equations, exact solution, generalized tanh function.