A novel (2+1)-dimensional complex coupled dispersionless system: Darboux transformation and multisolitons

doi:10.1088/1674-1056/adceff

Abstract This study presents a (2+1)-dimensional complex coupled dispersionless system. A Lax pair is proposed, and the Darboux transformation is employed to construct multisoliton solutions. These solutions exhibit a range of wave phenomena, including bright and dark solitons, S-shaped formations, parabolic profiles, and periodic wave patterns. Additionally, it is shown that the system is equivalent to the sine-Gordon equation and the negative flow of the modified Korteweg-de Vries hierarchy through appropriate transformations.

Keywords: integrable systems Darboux transformation solitons

Received: 12 March 2025
Revised: 03 April 2025
Accepted manuscript online: 22 April 2025

PACS:	05.45.Yv	(Solitons)
	03.30.Kk
	02.30.Jr	(Partial differential equations)

Corresponding Authors: H. W. A. Riaz, Ji Lin
E-mail: wajahat@zjnu.edu.cn;linji@zjnu.edu.cn

Cite this article:

H. W. A. Riaz and Ji Lin(林机) A novel (2+1)-dimensional complex coupled dispersionless system: Darboux transformation and multisolitons 2025 Chin. Phys. B 34 090502

[1] Kivshar Y S and Agrawal G P 2003 Optical solitons: from fibers to photonic crystals (Academic Press)
[2] Malomed B A 2014 The Sine-Gordon Model and Its Applications: From Pendula and Josephson Junctions to Gravity and High-Energy Physics 1-30
[3] Ablowitz M J and Clarkson P A 1991 Solitons, nonlinear evolution equations and inverse scattering, Vol. 149 (Cambridge University Press)
[4] Wang D S, Zhu C and Zhu X 2025 J. Differ. Equ. 416 642
[5] Zhang G and Yan Z 2020 Physica D 402 132170
[6] Ma X and Zhu J 2023 Stud. Appl. Math. 151 676
[7] Liu S, Tian B and Wang M 2021 Eur. Phys. J. Plus 136 1
[8] Xu G q 2019 Appl. Math. Lett. 97 81
[9] Konno K and Wadati M 1975 Prog. Theor. Phys. 53 1652
[10] Gao X Y, Guo Y J and Shan W R 2022 Chaos, Solitons and Fractals 162 112486
[11] Xie W K and Fan F C 2023 J. Math. Anal. Appl. 525 127251
[12] Belokolos E D, Bobenko A I, Enolskii V Z, Its A R and Matveev V B 1994 Algebro-geometric approach to nonlinear integrable equations, Vol. 550 (Springer-Verlag)
[13] Moretlo T, Adem A R and Muatjetjeja B 2022 Commun. Nonlinear Sci. Numer. Simul. 106 106072
[14] Yao Y, Yi H, Zhang X and Ma G 2023 Chin. Phys. Lett. 40 100503
[15] Shao H and Sudao B 2023 Chin. Phys. B 32 050204
[16] Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Springer Berlin Heidelberg)
[17] Riaz H W A, Lin J and Wang J 2024 Phys. Lett. A 528 130060
[18] Riaz H W A and Lin J 2024 Appl. Math. Lett. 158 109217
[19] Wen X Y, Lin Z and Wang D S 2024 Phys. Rev. E 109 044215
[20] Takasaki K and Takebe T 1995 Rev. Math. Phys. 7 743
[21] Calderbank D M and Kruglikov B 2021 Commun. Math. Phys. 382 1811
[22] Konno K and Oono H 1994 J. Phys. Soc. Jpn. 63 377
[23] Kakuhata H and Konno K 1996 J. Phys. Soc. Jpn. 65 340
[24] Kakuhata H and Konno K 1999 J. Phys. Soc. Jpn. 68 757
[25] Kotlyarov V P 1994 J. Phys. Soc. Jpn. 63 3535
[26] Shen S, Feng B F and Ohta Y 2016 Stud. Appl. Math. 136 64
[27] Riaz H W A and ul Hassan M 2018 J. Math. Anal. Appl. 458 1639
[28] Eren K and Ersoy S 2023 Complex Var. Elliptic Equ. 68 1984
[29] Wang G, Yang K, Gu H, Guan F and Kara A 2020 Nucl. Phys. B 953 114956
[30] Anco S C and Wolf T 2005 J. Nonllinear Math. Phys. 12 13
[31] Gelfand I, Gelfand S, Retakh V and Wilson R L 2005 Adv. Math. 193 56
[32] Pogrebkov A K 2014 Theor. Math. Phys. 181 1585

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A novel (2+1)-dimensional complex coupled dispersionless system: Darboux transformation and multisolitons

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