Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

doi:10.1088/1674-1056/ac4cc5

Abstract Rogue waves are a class of nonlinear waves with extreme amplitudes, which usually appear suddenly and disappear without any trace. Recently, the parity-time ($\mathcal {PT}$)-symmetric vector rogue waves (RWs) of multi-component nonlinear Schrödinger equation ($n$-NLSE) are usually derived by the methods of integrable systems. In this paper, we utilize the multi-stage physics-informed neural networks (MS-PINNs) algorithm to derive the data-driven $\mathcal {PT}$ symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition. The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.

Keywords: nonlinear Schrödinger equation vector rogue waves deep learning numerical simulations

Received: 22 November 2021
Revised: 05 January 2022
Accepted manuscript online: 24 January 2022

PACS:	02.30.Ik	(Integrable systems)
	02.60.Cb	(Numerical simulation; solution of equations)
	07.05.Mh	(Neural networks, fuzzy logic, artificial intelligence)

Fund: Project supported by National Natural Science Foundation of China (Grant Nos. 11771151, 61571005, and 61901160), the Science and Technology Program of Guangzhou (Grant No. 201904010362), and the Fundamental Research Program of Guangdong Province, China (Grant No. 2020B1515310023).

Corresponding Authors: De-Lu Zeng
E-mail: dlzeng@scut.edu.cn

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Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉) Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation 2022 Chin. Phys. B 31 060201

[1] Draper L 1967 Mar. Geol. 5 133
[2] Parkins A S and Walls D F 1998 Phys. Rep. 303 1
[3] Agrawal G P 2001 Nonlinear Fiber Optics, 3rd edn. (San Diego: Academic Press) pp. 195-211
[4] Peregrine D H 1983 ANZIAM J. 25 16
[5] Zabusky N J and Martin D K 1965 Phys. Rev. Lett. 15 240
[6] Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054
[7] Zakharov V E and Ostrovsky L A 2009 Physica D 238 p. 540
[8] Akhmediev N, Adrian A and Soto-Crespo J M 2009 Phys. Rev. E 80 026601
[9] Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110202
[10] Guo B L, Tian L X, Yan Z Y, Ling L M and Wang Y F 2017 Rogue Waves (Berlin: De Gruyter)
[11] Ling L M, Zhao L C and Guo B L 2016 Commun. Nonlinear Sci. Numer. Simul. 32 285
[12] Shabat A and Zakharov V 1972 JETP Lett. 34 62
[13] Calini A and Schober C M 2008 Extreme Ocean Waves p. 31
[14] Ohta Y and Yang J K 2012 P. Roy. Soc. A-Math. P. 468 1716
[15] Zhang X E and Chen Y 2018 Nonlinear Dyn. 93 2169
[16] Feng B F, Ling L M and Daisuke A T 2020 Stud. Appl. Math. 144 46
[17] Zhang G Q, Ling L M, Yan Z Y and Konotop V V 2021 Chaos 31 063120
[18] Zhang G Q, Ling L M and Yan Z Y 2021 J. Nonlinear Sci. 31 1
[19] Yang B and Yang J K 2020 J. Math. Anal. Appl. 487 124023
[20] Goodfellow I, Bengio Y and Courville A 2016 Deep Learning (Cambridge: The MIT Press)
[21] AnzaiAnzai Y 2012 Pattern recognition and machine learning (Morgan Kaufmann Publishers)
[22] Deng L, Hinton G and Kingsbury B 2013 Proc. IEEE Int. Conf. Acoust Speech Signal Process p. 8599
[23] Collobert R, Weston J, Bottou L, Karlen M, Kavukcuoglu, K and Kuksa P 2011 J. Mach. Learn. Res. 12 2493
[24] Krizhevsky A, Sutskever I and Hinton G E 2012 Adv. Neural Inf. Process Syst. 25 1097
[25] Hornik K, Stinchcombe M and White H 1989 Neural Networks 2 359
[26] Lagaris I E, Likas A and Fotiadis D I 1998 IEEE Trans. Neural Netw. 9 987
[27] Sirignano J and Spiliopoulos K 2018 J. Comput. Phys. 375 1339
[28] Raissi M, Perdikaris P and Karniadakis G E 2019 J. Comput. Phys. 378 686
[29] Baydin A G, Pearlmutter B A, Radul A A and Siskind J M 2018 J. Mach. Learn. Res. 18 1
[30] Pang G F, Lu L and Karniadakis G E 2019 SIAM J. Sci. Comput. 41 A2603
[31] Dwivedi V, Parashar N and Srinivasan B 2019 arXiv: 1907.08967
[32] Pang G, D'Elia M, Parks M and Karniadakis G E 2020 J. Comput. Phys. 422 109760
[33] Meng X, Li Z, Zhang D and Karniadakis G E 2020 Comput. Methods Appl. Mech. Eng. 370 113250
[34] Jagtap A D and Karniadakis G E 2020 J. Comput. Phys. 28 2002
[35] Lin S N and Chen Y 2107 arXiv: 2107.01009
[36] Pu J C, Peng W Q and Chen Y 2021 Wave Motion 107 102823
[37] Pu J C, Li J and Chen Y 2021 Chin. Phys. B 30 060202
[38] Pu J C and Chen Y 2109 arXiv: 2109.09266
[39] Wang R Q, Ling L M, Zeng D L and Feng B F 2021 Commun. Nonlinear Sci. Numer. Simul. 101 105896
[40] Wang L and Yan Z Y 2021 Phys. Lett. A 404 127408
[41] Pu J C, Li J and Chen Y 2021 Chin. Phys. B 30 060202
[42] Mo Y F, Ling L M and Zeng D L 2022 Phys. Lett. A 421 127739
[43] Wight C L and Zhao J 2021 Commun. Comput. Phys. 29 930
[44] Lu L, Meng X, Mao Z and Karniadakis G E 2021 SIAM Review 63 208
[45] Wang S F, Teng Y J and Perdikaris P 2021 SIAM J. Sci. Comput. 43 A3055
[46] Peng W Q and Chen Y 2111 arXiv: 2111.12424
[47] Kingma D P and Ba J 2015 Anon. International Conference on Learning Representations (San Dego)
[48] Liu D C and Nocedal J 1989 Math. Program. 45 503
[49] Stein M 1987 Technometrics 29 143
[50] Zhao L C, Xin G G, Yang Z Y 2014 Phys. Rev. E 90 022918
[51] Ling L M, Zhao L C, Yang Z Y and Guo B L 2017 Phys. Rev. E 96 022211
[52] Cao Q H and Dai C Q 2021 Chin. Phys. Lett. 38 090501
[53] Zhang X M, Qin Y H, Ling L M and Zhao L C 2021 Chin. Phys. Lett. 38 090201
[54] Wang B, Zhang Z and Li B 2020 Chin. Phys. Lett. 37 030501
[55] Ma X R, Tu Z C and Ran S J 2021 Chin. Phys. Lett. 38 110301
[56] Zhang G Q and Yan Z Y 2018 Commun. Nonlinear Sci. Numer. Simul. 62 117

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Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

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