Approximation of the soliton solution for the generalized Vakhnenko equation

doi:10.1088/1674-1056/18/11/002

中国物理B ›› 2009, Vol. 18 ›› Issue (11): 4608-4612.doi: 10.1088/1674-1056/18/11/002

Approximation of the soliton solution for the generalized Vakhnenko equation

莫嘉琪

Department of Mathematics, Anhui Normal University, Wuhu 241000, China Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiaotong University, Shanghai 200240, China

收稿日期:2009-03-05 修回日期:2009-05-01 出版日期:2009-11-20 发布日期:2009-11-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 40876010), the Key Innovation Project of the Chinese Academy of Sciences (Grant No KZCX2-YW-Q03-08), LASG State Key Laboratory Special Fund, China, and in part by E-Institutes of Shanghai Municipal Education Commission, China (Grant No E03004).

Approximation of the soliton solution for the generalized Vakhnenko equation

Mo Jia-Qi (莫嘉琪)

Department of Mathematics, Anhui Normal University, Wuhu 241000, China Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiaotong University, Shanghai 200240, China

Received:2009-03-05 Revised:2009-05-01 Online:2009-11-20 Published:2009-11-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 40876010), the Key Innovation Project of the Chinese Academy of Sciences (Grant No KZCX2-YW-Q03-08), LASG State Key Laboratory Special Fund, China, and in part by E-Institutes of Shanghai Municipal Education Commission, China (Grant No E03004).

摘要/Abstract

摘要： A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemko equation is obtained. By this method an arbitrary order approximation can be easily obtained and, similarly, approximate soliton solutions of other nonlinear equations can be acquired.

Abstract: A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemko equation is obtained. By this method an arbitrary order approximation can be easily obtained and, similarly, approximate soliton solutions of other nonlinear equations can be acquired.

Key words: homotopic mapping, soliton, Vakhnemko equation

中图分类号: (Solitons)

05.45.Yv

02.30.Uu (Integral transforms) 02.30.Nw (Fourier analysis) 02.30.Jr (Partial differential equations)

莫嘉琪. Approximation of the soliton solution for the generalized Vakhnenko equation[J]. 中国物理B, 2009, 18(11): 4608-4612.

Mo Jia-Qi (莫嘉琪). Approximation of the soliton solution for the generalized Vakhnenko equation[J]. Chin. Phys. B, 2009, 18(11): 4608-4612.

[1]	Wei Qi(漆伟), Xiao-Gang Guo(郭晓刚), Liang-Wei Dong(董亮伟), and Xiao-Fei Zhang(张晓斐). Modulational instability of a resonantly polariton condensate in discrete lattices[J]. 中国物理B, 2023, 32(3): 30502-030502.
[2]	Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems[J]. 中国物理B, 2023, 32(3): 30506-030506.
[3]	Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation[J]. 中国物理B, 2023, 32(3): 30505-030505.
[4]	Wen-Xiu Ma(马文秀). Matrix integrable fifth-order mKdV equations and their soliton solutions[J]. 中国物理B, 2023, 32(2): 20201-020201.
[5]	Nkeh Oma Nfor, Patrick Guemkam Ghomsi, and Francois Marie Moukam Kakmeni. Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane[J]. 中国物理B, 2023, 32(2): 20504-020504.
[6]	D Chevizovich, S Zdravković, A V Chizhov, and Z Ivić. Charge self-trapping in two strand biomolecules: Adiabatic polaron approach[J]. 中国物理B, 2023, 32(1): 10506-010506.
[7]	Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation[J]. 中国物理B, 2023, 32(1): 10505-010505.
[8]	Jing Wang(王静), Hua Wu(吴华), and Da-Jun Zhang(张大军). Reciprocal transformations of the space-time shifted nonlocal short pulse equations[J]. 中国物理B, 2022, 31(12): 120201-120201.
[9]	Guofei Zhang(张国飞), Jingsong He(贺劲松), and Yi Cheng(程艺). Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation[J]. 中国物理B, 2022, 31(11): 110201-110201.
[10]	Jing Wang(王静), Xue-Li Ding(丁学利), and Biao Li(李彪). Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation[J]. 中国物理B, 2022, 31(10): 100502-100502.
[11]	Shu-Wen Guan(关淑文), Ling-Zheng Meng(孟令正), and Li-Chen Zhao(赵立臣). Oscillation properties of matter-wave bright solitons in harmonic potentials[J]. 中国物理B, 2022, 31(8): 80506-080506.
[12]	Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯). Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters[J]. 中国物理B, 2022, 31(8): 80202-080202.
[13]	Hong-Cai Ma(马红彩), Yi-Dan Gao(高一丹), and Ai-Ping Deng(邓爱平). Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation[J]. 中国物理B, 2022, 31(7): 70201-070201.
[14]	Ahmet Bekir and Emad H M Zahran. Nonlinear dynamical wave structures of Zoomeron equation for population models[J]. 中国物理B, 2022, 31(6): 60401-060401.
[15]	Xi-zhong Liu(刘希忠) and Jun Yu(俞军). A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis[J]. 中国物理B, 2022, 31(5): 50201-050201.

Approximation of the soliton solution for the generalized Vakhnenko equation

Approximation of the soliton solution for the generalized Vakhnenko equation

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0