Exact Periodic Solitary Solutions to the Shallow Water Wave Equation
LI Dong-Long1, ZHAO Jun-Xiao2,3
1Department of Information and Computation Science, Guangxi University of Technology, Liuzhou 5450062Institute of Applied Physics and Computational Mathematics, Beijing 1000883School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049
Exact Periodic Solitary Solutions to the Shallow Water Wave Equation
LI Dong-Long1, ZHAO Jun-Xiao2,3
1Department of Information and Computation Science, Guangxi University of Technology, Liuzhou 5450062Institute of Applied Physics and Computational Mathematics, Beijing 1000883School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049
摘要Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.
Abstract：Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.
LI Dong-Long;ZHAO Jun-Xiao;. Exact Periodic Solitary Solutions to the Shallow Water Wave Equation[J]. 中国物理快报, 2009, 26(5): 54701-054701.
LI Dong-Long, ZHAO Jun-Xiao,. Exact Periodic Solitary Solutions to the Shallow Water Wave Equation. Chin. Phys. Lett., 2009, 26(5): 54701-054701.
[1] Ablowitz M J et al 1974 Appl. Math. 53 249 [2] Hirota R and Satsuma J 1976 J. Phys. Soc. Jpn. 40 611 [3] Hirota R 2004 The Direct Method in Soliton Theory(Cambridge: Cambridge University) [4] Hirota R 1971 Phys. Rev. Lett. 27 1192 [5] Hirota R 1980 Direct Method in Soliton Theory edBullough R K and Caudrey P J (Berlin: Springer) [6] Hirota R et al 1976 Prog. Theor. Phys. Suppl. 59 64 [7] Sawada K and Kotera T 1974 Prog. Theor. Phys. 51 1355 [8] Matsuno Y 1984 Bilinear Transformation Method (NewYork: Academic) [9] Huibin L et al 1990 J. Phys. A: Math. Gen. 234097 [10] Lv Z S and Zhang H Q 2003 Phys. Lett. A 307269 [11] Tian B et al 1996 Comput. Phys. Commun. 95139 [12] Malfliet W 2004 J. Comput. Appl. Math. 529164 [13] Wang M L 1996 Phys. Lett. A 213 279 [14] Ablowitz M J et al 1996 Comput. Phys. 126 299 [15] Senthilvela M 2001 Appl. Math. Comput. 123381 [16] Dai Z, Huang J and Jiang M 2006 Phys. Lett. A 352 411 [17] Dai Z, Li Z, Liu Z and Li D 2007 Physica A 384 285 [18] Dai Z, Liu Z 2008 Phys. Lett. A 2008 3725984 [19] Dai Z, Liu Z and Li D 2008 Chin. Phys. Lett. 25 1531 [20] Li D, Dai Z and Guo Y 2008 Chin. Phys. Lett. 25 4189
2009, Vol. 26 
