Approximate Solution of Homotopic Mapping to Solitary Wavefor Generalized Nonlinear KdV System
MO Jia-Qi
1Department of Mathematics, Anhui Normal University, Wuhu 2410002Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiaotong University, Shanghai 200240
Approximate Solution of Homotopic Mapping to Solitary Wave for Generalized Nonlinear KdV System
MO Jia-Qi
1Department of Mathematics, Anhui Normal University, Wuhu 2410002Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiaotong University, Shanghai 200240
摘要We study a generalized nonlinear KdV system is studied by using the homotopic mapping method. Firstly, a homotopic mapping transform is constructed; secondly, the suitable initial approximation is selected; then the homotopic mapping is used. The accuracy of the approximate solution for the solitary wave is obtained. From the obtained approximate solution, the homotopic mapping method exhibits a good accuracy.
Abstract：We study a generalized nonlinear KdV system is studied by using the homotopic mapping method. Firstly, a homotopic mapping transform is constructed; secondly, the suitable initial approximation is selected; then the homotopic mapping is used. The accuracy of the approximate solution for the solitary wave is obtained. From the obtained approximate solution, the homotopic mapping method exhibits a good accuracy.
[1] Ma S H, Qiang J Y and Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [2] Ma S H, Qiang J Y, Fang and J P 2007 Commun. Theor.Phys. 48 662 [3] Loutsenko I 2006 Commun. Math. Phys. 268 465 [4] Gedalin M 1998 Phys. Plasmas 5 127 [5] Parkes E J 2008 Chaos Solitons Fractals 38 154 [6] Li X Z and Wang M L 2007 Phys. Lett. A 361 115 [7] Wang M L 1995 Phys. Lett. A 199 169 [8] Sirendaoreji J S 2003 Phys. Lett. A 309 387 [9] McPhaden M J, Zhang D 2002 Nature 415 603 [10] Gu D F and Philander S G H 1997 Science 275805 [11] Pan L X, Zuo W M and Yan J R 2005 Acta Phys. Sin 54 1 (in Chinese) [12] Liao S J 2004 Beyond Perturbation: Introduction tothe Homotopy Analysis Method (New York: CRC) [13] He J H 2002 Approximate Analytical Methods inEngineering and Sciences (Shengzhou: Henan Science and TechnologyPress) (in Chinese) [14] Ni W M and Wei J C 2006 J. Differ. Equations 221 158 [15] Bartier J P 2006 Asymptotic Anal. 46 325 [16] Llibre J and de Silva P R 2007 J. Dyn. Differ.Equations 19 309 [17] Guarguaglini F R and Natalini R 2007 Commun. PartialDiffer. Equations 32 163 [18] Mo J Q 1989 Sci. Chin. A 32 1306 [19] Mo J Q and Lin W T 2008 J. Sys. Sci. Complexity 20 119 [20] Mo J Q and Wang H 2007 Acta Ecolog. Sin. 274366 [21] Mo J Q, Zhu J and Wang H 2003 Prog. Nat. Sci. 13 768 [22] Mo J Q, Zhang W J and He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [23] Mo J Q, Zhang W J and Chen X F 2007 Acta Phys.Sin. 56 6169 (in Chinese) [24] Mo J Q, Zhang W J and He M 2006 Acta Phys. Sin. 55 3233 (in Chinese) [25] Mo J Q, Lin W T and Wang H 2008 Chin. GeographicalSci 18 193 [26] Mo J Q, Lin W T and Wang H 2007 Prog. Nat. Sci. 17 230 [27] Mo J Q, Lin W T and Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) [28] Mo J Q, Wang H, Lin W T and Lin Y H 2006 Chin. Phys 15 671 [29] Mo J Q, Lin W T and Wang H 2007 Chin. Phys. 16 951 [30] Mo J Q and Lin W T 2008 Chin. Phys. 17 370 [31] Ma S H, Fang J P and Zheng C L 2008 Chin. Phys. 17 2767
2009, Vol. 26 
