Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(4): 040203    DOI: 10.1088/1674-1056/ac960a
GENERAL Prev   Next  

Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions

Sha Li(李莎)1, Tiecheng Xia(夏铁成)1,†, and Hanyu Wei(魏含玉)2
1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
2 College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Abstract  We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach. The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair. Subsequently, in the case that the Riemann-Hilbert problem is irregular, the N-soliton solutions of the equation can be deduced. In addition, the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.
Keywords:  complex Sharma-Tasso-Olver equation      Riemann-Hilbert problem      spectral problem      soliton solutions  
Received:  05 August 2022      Revised:  27 September 2022      Accepted manuscript online:  29 September 2022
PACS:  02.30.Rz (Integral equations)  
  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11975145), the Program for Science & Technology Innovation Talents in Universities of Henan Province, China (Grant No. 22HASTIT019), the Natural Science Foundation of Henan, China (Grant No. 202300410524), the Science and Technique Project of Henan, China (Grant No. 212102310397), the Academic Degrees & Graduate Education Reform Project of Henan Province, China (Grant No. 2021SJGLX219Y).
Corresponding Authors:  Tiecheng Xia     E-mail:

Cite this article: 

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 2023 Chin. Phys. B 32 040203

[1] Tasso H 1976 Cole's ansatz and extensions of Burgers' equation, January 1, 1976, Garching/Muenchen (Germany), Report No. IPP6/142
[2] Tasso H 1996 J. Phys. A: Math. Gen. 29 7779
[3] Lian Z J and Lou S Y 2005 Nonlinear Anal. 63 e1167
[4] Verheest F and Hereman W 1982 J. Phys. A: Math. Gen. 15 95
[5] Wazwaz A M 2007 Appl. Math. Comput. 188 1205
[6] Yang Z J 1994 J. Phys. A: Math. Gen. 27 2837
[7] Ugurlu Y and Kaya D 2007 Phys. Lett. A 370 251
[8] Inan I E and Kaya D 2007 Physica A 381 104
[9] Wang S, Tang X Y and Lou S Y 2004 Chaos Solitons Fract. 21 231
[10] Gudkov V V 1997 J. Math. Phys. 38 4794
[11] Shang Y D, Qin, J H, Huang Y and Yuan W J 2008 Appl. Math. Comput. 202 532
[12] Fan E G 2001 J. Math. Phys. 42 4327
[13] Shang Y D 2008 Chaos Solitons Fract. 36 762
[14] Hereman W, Banerjee P P, Korpel A, et al. 1986 J. Phys. A: Math. Gen. 19 607
[15] Zhang N, Xia T C and Hu B B 2017 Theor. Phys. 68 580
[16] Yue C and Xia T C 2014 J. Math. Phys. 55 083511
[17] Chen S J and Lü X 2022 Chaos Solitons Fract. 163 112543
[18] Wazwaz A M 2007 Appl. Math. Comput. 190 633
[19] Zhao Y W, Xia J W and Lü X 2022 Nonlinear Dyn. 108 4195
[20] Ablowitz M J, Kaup D J, Newell A C and Segur H 1974 Stud. Appl. Math. 53 249
[21] Chen S J and Lü X 2022 Commun. Nonlinear Sci. Numer. Simul. 109 106103
[22] Zhang Y, Cheng Z L and Hao X H 2012 Chin. Phys. B 21 120203
[23] Novikov S, Manakov S, Pitaevskii L and Zakharov V 1984 Theory of solitons: the inverse scattering method (New York: Springer)
[24] Ma W X 2019 Nonlinear Anal. 47 1
[25] Kang Z Z and Xia T C 2019 Chin. Phys. Lett. 36 110201
[26] Wang D S, Yin S J, Tian Y and Liu Y F 2014 Appl. Math. Comput. 229 296
[27] Li J and Xia T C 2021 Appl. Math. Lett. 113 106850
[28] Geng X G and Wu J P 2016 Wave Motion 60 62
[29] Kang Z Z, Xia T C and Ma X 2018 Chin. Phys. B 27 070201
[30] Li W and Liu Y P 2020 Mod. Phys. Lett. B 34 2050221
[31] Li J and Xia T C 2021 J. Math. Anal. Appl. 500 125109
[32] Xu S Q and Geng X G 2018 Chin. Phys. B 27 120202
[33] Li Y, Li J and Wang R Q 2021 Nonlinear Dyn. 105 1765
[34] Hu J, Xu J and Yu G F 2018 J. Nonlinear Math. Phys. 25 633
[35] Wen L L, Zhang N and Fan E G 2020 Acta Math. Sci. 40 113
[1] Matrix integrable fifth-order mKdV equations and their soliton solutions
Wen-Xiu Ma(马文秀). Chin. Phys. B, 2023, 32(2): 020201.
[2] Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation
Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Chin. Phys. B, 2023, 32(1): 010505.
[3] Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation
Guofei Zhang(张国飞), Jingsong He(贺劲松), and Yi Cheng(程艺). Chin. Phys. B, 2022, 31(11): 110201.
[4] Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints
Jun-Cai Pu(蒲俊才), Jun Li(李军), and Yong Chen(陈勇). Chin. Phys. B, 2021, 30(6): 060202.
[5] 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.
[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] (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] A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures
Zhai Yun-Yun (翟云云), Geng Xian-Guo (耿献国), He Guo-Liang (何国亮). Chin. Phys. B, 2014, 23(6): 060201.
[10] Periodic solitons in dispersion decreasingfibers with a cosine profile
Jia Ren-Xu (贾仁需), Yan Hong-Li (闫宏丽), Liu Wen-Jun (刘文军), Lei Ming (雷鸣). Chin. Phys. B, 2014, 23(10): 100502.
[11] Matter-wave solutions of Bose–Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields
Etienne Wamba, Timolėon C. Kofanė, and Alidou Mohamadou . Chin. Phys. B, 2012, 21(7): 070504.
[12] An extension of the modified Sawada–Kotera equation and conservation laws
He Guo-Liang(何国亮) and Geng Xian-Guo(耿献国) . Chin. Phys. B, 2012, 21(7): 070205.
[13] Riemann theta function periodic wave solutions for the variable-coefficient mKdV equation
Zhang Yi (张翼), Cheng Zhi-Long (程智龙), Hao Xiao-Hong (郝晓红). Chin. Phys. B, 2012, 21(12): 120203.
[14] Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation
Hu Xiao(胡晓) and Li Biao(李彪). Chin. Phys. B, 2011, 20(5): 050315.
[15] Discrete integrable system and its integrable coupling
Li Zhu(李柱). Chin. Phys. B, 2009, 18(3): 850-855.
No Suggested Reading articles found!