Darboux transformation and soliton solutions of a nonlocal Hirota equation

doi:10.1088/1674-1056/ac11e9

Abstract Starting from local coupled Hirota equations, we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz-Kaup-Newell-Segur scattering problem. The Lax integrability of the nonlocal Hirota equation is also guaranteed by existence of the Lax pair. By Lax pair, an n-fold Darboux transformation is constructed for the nonlocal Hirota equation by which some types of exact solutions are found. The solutions with specific properties are distinct from those of the local Hirota equation. In order to further describe the properties and the dynamic features of the solutions explicitly, several kinds of graphs are depicted.

Keywords: nonlocal Hirota equation Darboux transformation Lax pair soliton soultion

Received: 11 June 2021
Revised: 28 June 2021
Accepted manuscript online: 07 July 2021

PACS:	02.30.Jr	(Partial differential equations)
	04.20.Jb	(Exact solutions)
	11.10.Lm	(Nonlinear or nonlocal theories and models)

Fund: The project was supported by the National Natural Science Foundation of China (Grant Nos. 12001424, 11471004, and 11775047), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2021JZ-21), the Chinese Post doctoral Science Foundation (Grant No. 2020M673332), the Research Award Foundation for Outstanding Young Scientists of Shandong Province, China (Grant No. BS2015SF009), and the Three-Year Action Plan Project of Xi'an University (Grant No. 21XJZZ0001-01).

Corresponding Authors: Ruoxia Yao
E-mail: rxyao@snnu.edu.cn

Cite this article:

Yarong Xia(夏亚荣), Ruoxia Yao(姚若侠), and Xiangpeng Xin(辛祥鹏) Darboux transformation and soliton solutions of a nonlocal Hirota equation 2022 Chin. Phys. B 31 020401

[1] Huang L L and Mu C L 2020 J. Differ. Equation 269 6794
[2] Ablowitz M J, Luo X D and Musslimani Z H 2020 Nonlinearity 33 3653
[3] Liu Y K and Li B 2020 Nonlinear Dynam. 100 3717
[4] Chen J C, Yan Q X and Zhang H 2020 Appl. Math. Lett. 106 106375
[5] Chen J C and Yan Q X 2020 Nonlinear Dynam. 100 2807
[6] Wang Q and Liang G 2020 J. Opt. 22 055501
[7] Shen W, Ma Z Y, Fei J X, Zhu Q Y and Chen J C 2020 Complexity 2020 2370970
[8] Su J J and Zhang S 2021 Appl. Math. Lett. 112 106714
[9] Lou S Y 2020 Commun. Theor. Phys. 72 057001
[10] Ablowitz M J and Musslimani Z H 2013 Phys. Rev. Lett. 110 064105
[11] Sarma A K, Mohammad A M, Musslimani Z H and Christodoulides D N 2014 Phys. Rev. E 89 052918
[12] Khara A and Saxena A 2015 J. Math. Phys. 56 032104
[13] Fokas A S 2016 Nonlinearity 29 319
[14] Li M and Xu T 2015 Phys. Rev. E 91 033202
[15] Ma L Y and Zhu Z N 2016 J. Math. Phys. 57 064105
[16] Rao J G, Cheng Y and He J S 2017 Stud. Appl. Math. 139 568
[17] Ablowitz M J, Feng B F and Luo X D 2018 Stud. Appl. Math. 141 267
[18] Ha J T, Zhang H Q and Zhao Q L 2019 J. Appl. Anal. Comput. 9 200
[19] Xin X P, Xia Y R, Liu H Z and Zhang L L 2020 J. Math. Anal. Appl. 490 124227
[20] Yuan C L and Wen X Y 2021 Chin. Phys. B 30 060201
[21] Song C Q and Zhu Z N 2020 Acta Phys. Sin. 69 010204 (in Chinese)
[22] Ablowitz M J, Kaup D J, Newell A C and Segur H 1973 Phys. Rev. Lett. 31 125
[23] Zhang Y, Dong K H and Jin R J 2013 AIP Conf. Proc. 1562 249
[24] Huang X and Ling L M 2016 Eur. Phys. J. Plus 131 1
[25] Ye R S and Zhang Y 2020 Stud. Appl. Math. 145 197
[26] Du Z, Tian B, Qu Q X and Zhao X H 2020 Chin. Phys. B 29 030202
[27] Wazwaz A M 2020 Comput. Math. Appl. 79 1145
[28] Ma W X 2019 J. Appl. Anal. Comput. 9 1319
[29] Wang W, Yao R X and Lou S Y 2020 Chin. Phys. lett. 37 100501
[30] Xia Y R, Yao R X and Xin X P 2020 J. Nonlinear Math. Phys. 27 581
[31] Xin X P, Zhang L H, Xia Y R and Liu H Z 2020 J. Appl. Anal. Comput. 10 2669
[32] Yin Y H, Chen S J and Lv X 2020 Chin. Phys. B 29 120502
[33] Lv X and Chen S J 2021 Nonlinear Dynam. 103 947
[34] Song M, Wang B D and Cao J 2020 Chin. Phys. B 29 100206
[35] Xia J W, Zhao Y W and Lv X 2020 Commun. Nonlinear Sci. Numer. Simul. 90 105260
[36] Xia Y R Xin X P and Zhang S L 2017 Chin. Phys. B 26 030202

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