Some discussions about the variable separating method for solving nonlinear models

doi:10.1088/1674-1056/19/5/050204

中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50204-050204.doi: 10.1088/1674-1056/19/5/050204

Some discussions about the variable separating method for solving nonlinear models

阮航宇

Department of Physics, Ningbo University, Ningbo 315211, China

收稿日期:2009-07-07 修回日期:2009-12-15 出版日期:2010-05-15 发布日期:2010-05-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10675065, 90503006 and 10735030) and the K.C.Wong Magna Fund in Ningbo University.

Some discussions about the variable separating method for solving nonlinear models

Ruan Hang-Yu(阮航宇)^†

Department of Physics, Ningbo University, Ningbo 315211, China

Received:2009-07-07 Revised:2009-12-15 Online:2010-05-15 Published:2010-05-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10675065, 90503006 and 10735030) and the K.C.Wong Magna Fund in Ningbo University.

摘要/Abstract

摘要： Through analysing the exact solution of some nonlinear models, the role of the variable separating method in solving nonlinear equations is discussed. We find that rich solution structures of some special fields of these equations come from the nonzero seed solution. However, these nonzero seed solutions is likely to result in the divergent phenomena for the other field component of the same equation. The convergence and the signification of all field components should be discussed when someone solves the nonlinear equation using the variable separating method.

Abstract: Through analysing the exact solution of some nonlinear models, the role of the variable separating method in solving nonlinear equations is discussed. We find that rich solution structures of some special fields of these equations come from the nonzero seed solution. However, these nonzero seed solutions is likely to result in the divergent phenomena for the other field component of the same equation. The convergence and the signification of all field components should be discussed when someone solves the nonlinear equation using the variable separating method.

Key words: variable separating method, nonzero seed solution, nonlinear equation

中图分类号: (Solitons)

05.45.Yv

02.30.Jr (Partial differential equations)

阮航宇. Some discussions about the variable separating method for solving nonlinear models[J]. 中国物理B, 2010, 19(5): 50204-050204.

Ruan Hang-Yu(阮航宇). Some discussions about the variable separating method for solving nonlinear models[J]. Chin. Phys. B, 2010, 19(5): 50204-050204.

参考文献 18

[1]	Gardner C S, Green J M, Kruskal M D and Miura R M 1967 Phys. Rev. Lett. 19 1095
[1a]	Hirota R 1971 Phys. Rev. Lett. 27 1192
[2]	Olver P J 1986 Application of Lie Group to Differential Equation (New York: Springer)
[2a]	Clarkson P A and Kruskal M D 1989 J. Math. Phys. 30 2201
[3]	Matveer V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin, Heidelberg: Springers Verlag)
[4]	Lou S Y and Ruan H Y 2001 J. Phys. A: Math. Gen. 34 305
[5]	Ruan H Y and Chen Y X 1999 Chin. Phys. 8 241
[5a]	Ruan H Y and Chen Y X 2001 Acta. Phys. Sin. 50 586 (in Chinese)
[6]	Ruan H Y and Chen Y X 2003 Acta Phys. Sin. 52 1313 (in Chinese)
[7]	Ruan H Y and Chen Y X 2002 Z. Naturforsoh 57a 948
[7a]	Ruan H Y and Chen Y X 2000 Phys. Rev. E 62 5738 Ruan H Y 2002 J. Phys. Soc. Jpn. 71 453
[8]	Tang X Y, Chen C L and Lou S Y 2002 J. Phys. A: Math. Gen. 35 L293
[8a]	Zhang J F and Han P 2002 Acta. Phys. Sin. 51 705 (in Chinese)
[8b]	Zheng C L, Zhang J F, Wu F M, Sheng Z M and Chen L Q 2003 Chin. Phys. 12 472
[9]	Lou S Y 2000 Phys. Lett. A 277 94
[10]	Ying J P and Lou S Y 2001 Z. Naturforsoh 56a 619
[11]	Tang X Y and Lou S Y 2002 Chaos, Solitons and Fractals 14 1451
[11a]	Tang X Y, Chen C L and Lou S Y 2002 J. Phys. A 35 L293
[12]	Ruan H Y 2003 Physica Scripta 47 240
[13]	Lou S Y and Hu X B 1997 J. Math. Phys. 38 6401
[14]	Zakharov V E 1968 J. Appl. Mech. Tech. Phys. (USSR) 9 190
[15]	Boiti M, Leon J J P and Pempinelli F 1987 Inverse Problems 3 371
[16]	Hirota R 1972 Phys. Rev. Lett. 27 1192
[17]	Zheng C L, Zhang J F and Chen L Q 2003 Commun. Theor. Phys. 40 385
[18]	Tang X Y and Lou S Y 2003 Commun. Theor. Phys. 40 62

Some discussions about the variable separating method for solving nonlinear models

Some discussions about the variable separating method for solving nonlinear models

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 18

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	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.
[2]	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.
[3]	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.
[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.