N-soliton solutions of an integrable equation studied by Qiao

doi:10.1088/1674-1056/22/4/040201

中国物理B ›› 2013, Vol. 22 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/22/4/040201

• GENERAL • 下一篇

N-soliton solutions of an integrable equation studied by Qiao

扎其劳

College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China

收稿日期:2012-08-09 修回日期:2012-10-08 出版日期:2013-03-01 发布日期:2013-03-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11261037), the High Education Science Research Rund of China (Grant No. 211034), and the High Education Science Research Program of Inner Mongolia Autonomous Region, China (Grant No. NJ10045).

N-soliton solutions of an integrable equation studied by Qiao

Zhaqilao (扎其劳)

College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China

Received:2012-08-09 Revised:2012-10-08 Online:2013-03-01 Published:2013-03-01
Contact: Zhaqilao E-mail:zhaqilao@imnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11261037), the High Education Science Research Rund of China (Grant No. 211034), and the High Education Science Research Program of Inner Mongolia Autonomous Region, China (Grant No. NJ10045).

摘要/Abstract

摘要： In this paper, we studied N-soliton solutions of a new integrable equation studied by Qiao [J. Math. Phys. 48 082701 (2007)]. Firstly, we employed the Darboux matrix method to construct a Darboux transformation for the modified Korteweg-de Vries equation. Then we use the Darboux transformation and a transformation, introduced by Sakovich [J. Math. Phys. 52 023509 (2011)], to derive N-soliton solutions of the new integrable equation from the seed solution. In particular, the multiple soliton solutions are explicitly obtained and shown through some figures.

关键词: soliton solution, Darboux transformation, integrable equation

Abstract: In this paper, we studied N-soliton solutions of a new integrable equation studied by Qiao [J. Math. Phys. 48 082701 (2007)]. Firstly, we employed the Darboux matrix method to construct a Darboux transformation for the modified Korteweg-de Vries equation. Then we use the Darboux transformation and a transformation, introduced by Sakovich [J. Math. Phys. 52 023509 (2011)], to derive N-soliton solutions of the new integrable equation from the seed solution. In particular, the multiple soliton solutions are explicitly obtained and shown through some figures.

Key words: soliton solution, Darboux transformation, integrable equation

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations) 05.45.Yv (Solitons)

扎其劳. N-soliton solutions of an integrable equation studied by Qiao[J]. 中国物理B, 2013, 22(4): 40201-040201.

Zhaqilao (扎其劳). N-soliton solutions of an integrable equation studied by Qiao[J]. Chin. Phys. B, 2013, 22(4): 40201-040201.

参考文献 25

[1]	Qiao Z J 2007 J. Math. Phys. 48 082701
[2]	Qiao Z J and Liu L P 2009 Chaos, Solitons & Fractals 41 587
[3]	Qiao Z J and Zhang G P 2006 Europhys. Lett. 73 657
[4]	Li J B and Qiao Z J 2010 J. Math. Phys. 51 042703
[5]	Sakovich S 2011 J. Math. Phys. 52 023509
[6]	Sakovich S Y 2003 Phys. Lett. A 314 232
[7]	Gu C H, Hu H S and Zhou Z X 2005 Darboux Transformations in Integrable Systems. Theory and Their Applications to Geometry (Dortrecht: Springer)
[8]	Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
[9]	Rogers C and Schief W K 2002 Bäcklund and Darboux Transformations Geometry and Modern Applications in Soliton Theory (Cambrige: Cambrige University Press)
[10]	Li Y S and Zhang J E 2003 Chaos, Solitons & Fractals 16 271
[11]	Lin J, Ren B, Li H M and Li Y S 2008 Phys. Rev. E 77 036605
[12]	Neugebauer G and Meinel R 1984 Phys. Lett. A 100 467
[13]	Levi D, Neugebauer G and Meinel R 1984 Phys. Lett. A 102 1
[14]	Geng X G and He G L 2010 J. Math. Phys. 51 033514
[15]	Fan E G 2001 Commun. Theor. Phys. 36 401
[16]	Li X M and Chen A H 2005 Phys. Lett. A 342 413
[17]	Huang D J, Li D S and Zhang H Q 2007 Chaos, Solitons & Fractals 33 1677
[18]	Zhaqilao and Li Z B 2009 J. Math. Anal. Appl. 359 794
[19]	Zhaqilao and Sirendaoreji 2010 J. Math. Phys. 51 073501
[20]	Zhaqilao and Sirendaoreji 2010 J. Math. Phys. 51 113507
[21]	Hu H C, Tang X Y, Lou S Y and Liu Q P 2004 Chaos, Solitons & Fractals 22 327
[22]	Li H Z, Tian B, Li L L, Zhang H Q and Xu T 2008 Phys. Scr. 78 065001
[23]	Zhaqilao, Zhao Y L and Li Z B 2009 Chin. Phys. B 18 1780
[24]	Zheng X Q and Liu J Y 2012 Chin. Phys. B 21 090202
[25]	Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)

N-soliton solutions of an integrable equation studied by Qiao

N-soliton solutions of an integrable equation studied by Qiao

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 25

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Feng Yuan(袁丰) and Behzad Ghanbari. Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations[J]. 中国物理B, 2023, 32(4): 40201-040201.
[2]	Sha Li(李莎), Tiecheng Xia(夏铁成), and Hanyu Wei(魏含玉). Riemann--Hilbert approach of the complex Sharma—Tasso—Olver equation and its N-soliton solutions[J]. 中国物理B, 2023, 32(4): 40203-040203.
[3]	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.
[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]	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.
[6]	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.
[7]	Yarong Xia(夏亚荣), Ruoxia Yao(姚若侠), and Xiangpeng Xin(辛祥鹏). Darboux transformation and soliton solutions of a nonlocal Hirota equation[J]. 中国物理B, 2022, 31(2): 20401-020401.
[8]	Jun-Cai Pu(蒲俊才), Jun Li(李军), and Yong Chen(陈勇). Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints[J]. 中国物理B, 2021, 30(6): 60202-060202.
[9]	Manna Chen(陈曼娜), Hongcheng Wang(王红成), Hai Ye(叶海), Xiaoyuan Huang(黄晓园), Ye Liu(刘晔), Sumei Hu(胡素梅), and Wei Hu(胡巍). Collapse arrest in the space-fractional Schrödinger equation with an optical lattice[J]. 中国物理B, 2021, 30(10): 104206-104206.
[10]	王丽丽, 刘文军. Stable soliton propagation in a coupled (2+1) dimensional Ginzburg-Landau system[J]. 中国物理B, 2020, 29(7): 70502-070502.
[11]	宋丽军, 徐晓雅, 王艳. Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation[J]. 中国物理B, 2020, 29(6): 64211-064211.
[12]	康周正, 夏铁成, 马茜. Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach[J]. 中国物理B, 2018, 27(7): 70201-070201.
[13]	徐思齐, 耿献国. N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method[J]. 中国物理B, 2018, 27(12): 120202-120202.
[14]	徐涛, 陈勇, 林机. Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics[J]. 中国物理B, 2017, 26(12): 120201-120201.
[15]	宋彩芹, 肖冬梅, 朱佐农. Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation[J]. 中国物理B, 2017, 26(10): 100204-100204.