Exact Periodic Solitary-Wave Solution for KdV Equation
DAI Zheng-De1,2, LIU Zhen-Jiang3, LI Dong-Long2
1School of Mathematics and Physics, Yunnan University, Kunming 6500912Department of Information and Computing Science, Guangxi Institute of Technology, Liuzhou 5450053Department of Mathematics, Qujing Normal University, Qujing 655000
Exact Periodic Solitary-Wave Solution for KdV Equation
DAI Zheng-De1,2;LIU Zhen-Jiang3;LI Dong-Long2
1School of Mathematics and Physics, Yunnan University, Kunming 6500912Department of Information and Computing Science, Guangxi Institute of Technology, Liuzhou 5450053Department of Mathematics, Qujing Normal University, Qujing 655000
摘要A new technique, the extended homoclinic test technique, is proposed to seek periodic solitary wave solutions of integrable systems. Exact periodic solitary-wave solutions for classical KdV equation are obtained using this technique. This result shows that it is entirely possible for the (1+1)-dimensional integrable equation that there exists a periodic solitary-wave.
Abstract：A new technique, the extended homoclinic test technique, is proposed to seek periodic solitary wave solutions of integrable systems. Exact periodic solitary-wave solutions for classical KdV equation are obtained using this technique. This result shows that it is entirely possible for the (1+1)-dimensional integrable equation that there exists a periodic solitary-wave.
[1] Ablowitz M J and Clarkson P A 1991 Solitons,Nonlinear Evolution Equations and Inverse Scattering (Cambridge:Cambridge University Press) [2] Gardner C S, Greene J M and Kruskal M D 1967 Phys. Rev.Lett. 19 1095 [3]Hirota R 1971 Phys. Rev. Lett. 27 1192 [4]Miurs M R 1978 Backlund Transformation (Berlin: Springer) [5]Weiss J, Tabor M and Garnevale G 1983 J. Math. Phys. 24 522 [6]Yan C 1996, Phys. Lett. A 224 77 [7]Wang M L 1996 Phys. Lett. A 213 279 [8]El-Shabed M 2005 Int. J. Nonlinear Sci. Numer. Simul. 6 163 [9]He J H 2005 Int. J. Nonlinear Sci. Numer. Simul. 6 207 [10]He J H 2006 Int. Modern Phys. B 20 1141 [11]He J H 1999 Int. J. Nonlinear Mech. 34 699 [12]He J H 2004 Chaos Solitons Frac. 19 847 [13]Abassy T A, El-Tawil M A and Saleh H K 2004 Int. J. Nonlinear Sci. Numer. Simul. 5 327 [14]Zayad E M E, Zedan H A and Gepreel K A 2004 Int. J. Nonlinear Sci. Numer. Simul. 5 221 [15]Zhang S and Xia T C 2006 Appl. Math. Comput. 181 319 [16]HumJ Q 2005 Chaos Solitons Fractals . 23 391 [17]Zhang S and Xia T C 2006 Phys. Lett. A 356 119 [18]Liu S K, Fu Z T and Zhao Q 2001 Phys. Lett. A 289 69 [19]Zhao X Q, Zhi H Y and Zhang H Q 2006 Chaos SolitonsFractals 28 112 [20]Liu J B and Yang K Q 2004 Chaos Solitons Frac. 22 111 [21]Zhang S 2007 Phys. Lett. A 365 448 [22]Shek E C M and Chow K W 2008 Chaos Solitons Fractals 36 296 [23]He J H and Wu X H 2006 Chaos Solitons Fractals 30 700 [24]Zhang S 2008 Appl. Math. Comput. 197 128 [25]Dai Z D, Huang J, Jiang M R and Wang S H 2005 Chaos Solitons Frac. 26 1189 [26]Dai Z D, Jiang M R, Dai Q Y and Li S L 2006 Chin. Phys.Lett. 23 1065 [27]Dai Z D, Huang J and Jiang M R 2006 Phys. Lett. A 352 411 [28]Dai Z D, Li S L, Li D L and Zhu A J 2007 Chin. Phys.Lett. 24 1429
2008, Vol. 25 
