Riemann-Hilbert problem for the defocusing Lakshmanan-Porsezian-Daniel equation with fully asymmetric nonzero boundary conditions

doi:10.1088/1674-1056/ad5af2

Abstract The Riemann-Hilbert approach is demonstrated to investigate the defocusing Lakshmanan-Porsezian-Daniel equation under fully asymmetric nonzero boundary conditions. In contrast to the symmetry case, this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces. For the direct problem, we analyze the Jost solution of lax pairs and some properties of scattering matrix, including two kinds of symmetries. The inverse problem at branch points can be presented, corresponding to the associated Riemann-Hilbert. Moreover, we investigate the time evolution problem and estimate the value of solving the solutions by Jost function. For the inverse problem, we construct it as a Riemann-Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan-Porsezian-Daniel equation. The solutions of the Riemann-Hilbert problem can be constructed by estimating the solutions. Finally, we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski-Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces. These results are valuable for understanding physical phenomena and developing further applications of optical problems.

Keywords: Riemann-Hilbert problem defocusing Lakshmanan-Porsezian-Daniel equation inverse scattering transform asymmetric nonzero boundary conditions

Received: 23 May 2024
Revised: 19 June 2024
Accepted manuscript online: 24 June 2024

PACS:	02.30.Rz	(Integral equations)
	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

Fund: This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2024MS126).

Corresponding Authors: Xiyang Xie
E-mail: xiyangxie@ncepu.edu.cn

Cite this article:

Jianying Ji(纪建英) and Xiyang Xie(解西阳) Riemann-Hilbert problem for the defocusing Lakshmanan-Porsezian-Daniel equation with fully asymmetric nonzero boundary conditions 2024 Chin. Phys. B 33 090201

[1] Qiu W X, Geng K L, Zhu B W, Liu W, Li J T and Dai C Q 2024 Nonlinear Dyn. 112 10215
[2] Xu S Y, Zhou Q and Liu W 2023 Nonlinear Dyn. 111 18401
[3] Leblond H 1998 J. Phys. A: Math. Gen. 31 3041
[4] Yin Y H and L¨u X 2024 Chaos Solitons Fractals 181 114595
[5] Rajan M S M, Mahalingam A and Uthayakumar A 2014 Ann. Phys. 346 1
[6] Congy T, El G A, Hoefer M A and Shearer M 2018 Stud. Appl. Math. 142 241
[7] Lazarides N and Kourakis I 2024 Nonlinear Dyn. 112 2795
[8] Chen J C, Feng B F and Maruno K T 2023 Physica D 448 133695
[9] Chen J C and Feng B F 2023 Stud. Appl. Math. 150 35
[10] Chen J C, Yang B and Feng B F 2023 Stud. Appl. Math. 151 1020
[11] Adhikari S K 2005 Phys. Lett. A 346 179
[12] Chen Y X 2023 Chaos Solitons Fractals 169 113251
[13] Ablowitz M J, Kaup D J, Newell A C and Segur H 1974 Stud. Appl. Math. 53 249
[14] Zakharov V E and Shabat A B 1972 Sov. Phys. JETP 34 62
[15] Ma W X 2022 Physica D 430 133078
[16] Demontis F, Prinari B, van der Mee C and Vitale F 2013 Stud. Appl. Math. 131 1
[17] Li S, Xia T C and Wei H Y 2023 Chin. Phys. B 32 040203
[18] Ma W X 2022 Chin. Phys. Lett. 39 100201
[19] Guo B L, Ling L M and Liu Q P 2012 Phys. Rev. E 85 026607
[20] Ma L Y, Shen S F and Zhu Z N 2017 J. Math. Phys. 58 103501
[21] Zhang C R, Tian B, Liu L, Chai H P and Yin H M 2020 Chaos Solitons Fractals 136 109763
[22] Ding C C, Zhou Q, Triki H and Hu Z H 2022 Opt. Express 30 40712
[23] Goodman R H, Holmes P J and Weinstein M I 2004 Physica D 192 215
[24] Yang J K 2019 Phys. Lett. A 383 328
[25] Santini P M 2018 J. Phys. A 51 495207
[26] Zhang Z C and Fan E G 2021 Z. Angew. Math. Phys. 72 153
[27] Zhang G and Yan Z 2020 Physica D 402 132170
[28] Zhao Y and Zhu D H 2023 arXiv:2312.10762[math-ph]
[29] Its A R and Ustinov A F 1986 Sov. Phys. Dokl. 31 893
[30] Vartanian A H 2000 Inverse Prob. 16 L39
[31] Vartanian A H 2002 Math. Phys. Anal. Geom. 5 319
[32] Zhang Y and Hao H Q 2024 Appl. Math. Lett. 153 109044
[33] Ma Y L and Li B Q 2024 Opt. Quantum Electron. 56 151
[34] Biondini G, Fagerstrom E and Prinari B 2016 Physica D 333 117
[35] Zhang G, Chen S and Yan Z Y 2020 Commun. Nonlinear Sci. Numer. Simulat. 80 104927
[36] Ye R S, Han P F and Zhang Y 2024 arXiv:2401.16684[nlin.SI]

[1]	Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions Luyao Zhang(张路瑶) and Xiyang Xie(解西阳). Chin. Phys. B, 2024, 33(9): 090207.
[2]	Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions Hui-Chao Zhao(赵会超), Lei-Nuo Ma(马雷诺), and Xi-Yang Xie(解西阳). Chin. Phys. B, 2024, 33(8): 080201.
[3]	Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions Sha Li(李莎), Tiecheng Xia(夏铁成), and Hanyu Wei(魏含玉). Chin. Phys. B, 2023, 32(4): 040203.
[4]	Matrix integrable fifth-order mKdV equations and their soliton solutions Wen-Xiu Ma(马文秀). Chin. Phys. B, 2023, 32(2): 020201.
[5]	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.
[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.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Riemann-Hilbert problem for the defocusing Lakshmanan-Porsezian-Daniel equation with fully asymmetric nonzero boundary conditions

Cite this article:

Online attention