Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(4): 040201    DOI: 10.1088/1674-1056/22/4/040201
GENERAL   Next  

N-soliton solutions of an integrable equation studied by Qiao

College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China
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.
Keywords:  soliton solution      Darboux transformation      integrable equation  
Received:  09 August 2012      Revised:  08 October 2012      Published:  01 March 2013
PACS:  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
  05.45.Yv (Solitons)  
Fund: 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).
Corresponding Authors:  Zhaqilao     E-mail:

Cite this article: 

Zhaqilao N-soliton solutions of an integrable equation studied by Qiao 2013 Chin. Phys. B 22 040201

[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)
[1] Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type
Cui-Lian Yuan(袁翠连) and Xiao-Yong Wen(闻小永). Chin. Phys. B, 2021, 30(3): 030201.
[2] Stable soliton propagation in a coupled (2+1) dimensional Ginzburg-Landau system
Li-Li Wang(王丽丽), Wen-Jun Liu(刘文军). Chin. Phys. B, 2020, 29(7): 070502.
[3] Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation
Li-Jun Song(宋丽军), Xiao-Ya Xu(徐晓雅), Yan Wang(王艳). Chin. Phys. B, 2020, 29(6): 064211.
[4] Rational solutions and interaction solutions for (2 + 1)-dimensional nonlocal Schrödinger equation
Mi Chen(陈觅) and Zhen Wang(王振). Chin. Phys. B, 2020, 29(12): 120201.
[5] Soliton molecules and dynamics of the smooth positon for the Gerdjikov–Ivanov equation
Xiangyu Yang(杨翔宇), Zhao Zhang(张钊), and Biao Li(李彪)†. Chin. Phys. B, 2020, 29(10): 100501.
[6] Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach
Zhou-Zheng Kang(康周正), Tie-Cheng Xia(夏铁成), Xi Ma(马茜). Chin. Phys. B, 2018, 27(7): 070201.
[7] N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method
Si-Qi Xu(徐思齐), Xian-Guo Geng(耿献国). Chin. Phys. B, 2018, 27(12): 120202.
[8] Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics
Tao Xu(徐涛), Yong Chen(陈勇), Ji Lin(林机). Chin. Phys. B, 2017, 26(12): 120201.
[9] Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation
Cai-Qin Song(宋彩芹), Dong-Mei Xiao(肖冬梅), Zuo-Nong Zhu(朱佐农). Chin. Phys. B, 2017, 26(10): 100204.
[10] Localized waves in three-component coupled nonlinear Schrödinger equation
Tao Xu(徐涛), Yong Chen(陈勇). Chin. Phys. B, 2016, 25(9): 090201.
[11] (2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect
Jin-Yuan Li(李近元), Nian-Qiao Fang(方念乔), Ji Zhang(张吉), Yu-Long Xue(薛玉龙), Xue-Mu Wang(王雪木), Xiao-Bo Yuan(袁晓博). Chin. Phys. B, 2016, 25(4): 040202.
[12] Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)
Wang Xin-Zeng, Dong Huan-He. Chin. Phys. B, 2015, 24(8): 080201.
[13] Rogue-wave pair and dark-bright-rogue wave solutions of the coupled Hirota equations
Wang Xin, Chen Yong. Chin. Phys. B, 2014, 23(7): 070203.
[14] Nonautonomous dark soliton solutions in two-component Bose-Einstein condensates with a linear time-dependent potential
Li Qiu-Yan, Wang Shuang-Jin, Li Zai-Dong. Chin. Phys. B, 2014, 23(6): 060310.
[15] Periodic solitons in dispersion decreasingfibers with a cosine profile
Jia Ren-Xu, Yan Hong-Li, Liu Wen-Jun, Lei Ming. Chin. Phys. B, 2014, 23(10): 100502.
No Suggested Reading articles found!