Please wait a minute...
Chin. Phys. B, 2017, Vol. 26(10): 100204    DOI: 10.1088/1674-1056/26/10/100204
GENERAL Prev   Next  

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)
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Abstract  The nonlinear Schrödinger (NLS) equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright-bright, bright-dark, and dark-dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright-bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright-bright or bright-dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.
Keywords:  multi-component NLS-Boussinesq equation      soliton solution      rogue wave solution  
Received:  04 August 2017      Revised:  14 August 2017      Published:  05 October 2017
PACS:  02.30.Ik (Integrable systems)  
  04.20.Jb (Exact solutions)  
  04.30.Nk (Wave propagation and interactions)  
  05.45.Yv (Solitons)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11371248, 11431008, 11271254, 11428102, and 11671255) and the Fund from the Ministry of Economy and Competitiveness of Spain (Grant Nos. MTM2012-37070 and MTM2016-80276-P (AEI/FEDER,EU)).
Corresponding Authors:  Zuo-Nong Zhu     E-mail:

Cite this article: 

Cai-Qin Song(宋彩芹), Dong-Mei Xiao(肖冬梅), Zuo-Nong Zhu(朱佐农) Soliton and rogue wave solutions of two-component nonlinear Schrödinger equation coupled to the Boussinesq equation 2017 Chin. Phys. B 26 100204

[1] Akhmediev N N and Ankiewicz A 1997 Solitons:nonlinear pulses and beams (Chapman & Hall)
[2] Kivshar Y S and Agrawal G 2003 Optical solitons:from fibers to photonic crystals (Academic Press)
[3] Scott A C 1984 Phys. Scr. 29 279.
[4] Makhankov V G 2012 Soliton phenomenology (Springer Science & Business Media)
[5] Ablowitz M J, Biondini G and Ostrovsky L A 2000 Chaos 10 471
[6] Ablowitz M J, Kaup D J and Newell A C 1974 Stud. Appl. Math. 53 249
[7] Zakharov V E and Shabat A B 1973 Sov. Phys. JETP 34 62
[8] Matveev V B and Salli M A 1991 Darboux Transformations and Solitons (Springer Series in Nonlinear Dynamics) (Berlin:Springer)
[9] Akhmediev N, Soto-Crespo J M and Ankiewicz A 2009 Phys. Lett. A 373 2137
[10] Yajima N and Oikawa M 1976 Prog. Theor. Phys. 56 1719
[11] Rao N N 1988 J. Plasma Phys. 39 385
[12] Hase Y and Satsuma J 1988 J. Phys. Soc. Jpn. 57 679
[13] Chowdhury A R and Rao N N 1998 Chaos, Solitons & Fractals 9 1747
[14] Hu X B, Guo B L and Tam H W 2003 J. Phys. Soc. Jpn. 72 189
[15] Mu G and Qin Z 2012 J. Phys. Soc. Jpn. 81 084001
[16] Wang C, Dai Z and Liu C 2014 Phys. Scr. 89 075206
[17] Prinari B, Ablowitz M J and Biondini G 2006 J. Math. Phys. 47 063508
[18] Kanna T and Lakshmanan M 2001 Phys. Rev. Lett. 86 5043
[19] Kanna T, Lakshmanan M, Dinda P T, et al. 2006 Phys. Rev. E 73 026604
[20] Baronio F, Degasperis A, Conforti M, et al. 2012 Phys. Rev. Lett. 109 044102
[21] Ling L, Zhao L C and Guo B 2016 Commun. Nonlinear Sci. Numer. Simul. 32 285
[22] Dean G, Klotz T, Prinari B, et al. 2013 Appl. Anal. 92 379
[23] Chan H N, Malomed B A, Chow K W, et al. 2016 Phys. Rev. E 93 012217
[24] Kanna T, Sakkaravarthi K and Tamilselvan K 2013 Phys. Rev. E 88 062921
[25] Yu G F and Lao D 2016 Commun. Nonlinear Sci. Numer. Simul. 30 196
[26] Feng B F 2015 Physica D 297 62
[27] Dudley J M, Genty G, Dias F, et al. 2009 Opt. Express 17 21497
[28] Zhang H Q, Yuan S S and Wang Y 2016 Mod. Phys. Lett. B 30 1650208
[29] Zhang H Q, Liu X L and Wen L L 2015 Z. Naturforsch. A 71 95
[30] Ohta Y and Yang J 2012 Proc. R. Soc. A 468 1716
[31] Guo B, Ling L and Liu Q P 2012 Phys. Rev. E 85 026607
[32] Ling L, Guo B and Zhao L C 2014 Phys. Rev. E 89 041201
[33] Yan Z 2010 Phys. Lett. A 374 672
[34] He J S, Zhang H R, Wang L H, Porsezian K and Fokas A S 2013 Phys. Rev. E 87 052914
[35] Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110202
[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] Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation
Haifeng Wang(王海峰), Yufeng Zhang(张玉峰). Chin. Phys. B, 2020, 29(4): 040501.
[5] 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.
[6] 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.
[7] A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation
Panfeng Zheng(郑攀峰), Man Jia(贾曼). Chin. Phys. B, 2018, 27(12): 120201.
[8] (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.
[9] 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.
[10] 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.
[11] Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions
Xu Gui-Qiong. Chin. Phys. B, 2013, 22(5): 050203.
[12] N-soliton solutions of an integrable equation studied by Qiao
Zhaqilao. Chin. Phys. B, 2013, 22(4): 040201.
[13] Nonautonomous solitons in the continuous wave background of the variable-coefficient higher-order nonlinear Schrödinger equation
Dai Chao-Qing, Chen Wei-Lu. Chin. Phys. B, 2013, 22(1): 010507.
[14] Matter-wave solutions of Bose–Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields
Etienne Wamba, Timoléon C. Kofané, Alidou Mohamadou . Chin. Phys. B, 2012, 21(7): 070504.
[15] Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential
Li Hua-Mei,Ge Long,He Jun-Rong. Chin. Phys. B, 2012, 21(5): 050512.
No Suggested Reading articles found!