Please wait a minute...
Chin. Phys. B, 2022, Vol. 31(6): 060201    DOI: 10.1088/1674-1056/ac4cc5
GENERAL Prev   Next  

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

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)
School of Mathematics, South China University of Technology, Guangzhou 510640, China
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:

Cite this article: 

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
[1] All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems
Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). Chin. Phys. B, 2023, 32(3): 030506.
[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] Deep-learning-based cryptanalysis of two types of nonlinear optical cryptosystems
Xiao-Gang Wang(汪小刚) and Hao-Yu Wei(魏浩宇). Chin. Phys. B, 2022, 31(9): 094202.
[4] Development of an electronic stopping power model based on deep learning and its application in ion range prediction
Xun Guo(郭寻), Hao Wang(王浩), Changkai Li(李长楷),Shijun Zhao(赵仕俊), Ke Jin(靳柯), and Jianming Xue(薛建明). Chin. Phys. B, 2022, 31(7): 073402.
[5] Fringe removal algorithms for atomic absorption images: A survey
Gaoyi Lei(雷高益), Chencheng Tang(唐陈成), and Yueyang Zhai(翟跃阳). Chin. Phys. B, 2022, 31(5): 050313.
[6] Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics
Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红). Chin. Phys. B, 2022, 31(3): 033101.
[7] Deep learning for image reconstruction in thermoacoustic tomography
Qiwen Xu(徐启文), Zhu Zheng(郑铸), and Huabei Jiang(蒋华北). Chin. Phys. B, 2022, 31(2): 024302.
[8] Learning physical states of bulk crystalline materials from atomic trajectories in molecular dynamics simulation
Tian-Shou Liang(梁添寿), Peng-Peng Shi(时朋朋), San-Qing Su(苏三庆), and Zhi Zeng(曾志). Chin. Phys. B, 2022, 31(12): 126402.
[9] RNAGCN: RNA tertiary structure assessment with a graph convolutional network
Chengwei Deng(邓成伟), Yunxin Tang(唐蕴芯), Jian Zhang(张建), Wenfei Li(李文飞), Jun Wang(王骏), and Wei Wang(王炜). Chin. Phys. B, 2022, 31(11): 118702.
[10] Effects of Prandtl number in two-dimensional turbulent convection
Jian-Chao He(何建超), Ming-Wei Fang(方明卫), Zhen-Yuan Gao(高振源), Shi-Di Huang(黄仕迪), and Yun Bao(包芸). Chin. Phys. B, 2021, 30(9): 094701.
[11] High speed ghost imaging based on a heuristic algorithm and deep learning
Yi-Yi Huang(黄祎祎), Chen Ou-Yang(欧阳琛), Ke Fang(方可), Yu-Feng Dong(董玉峰), Jie Zhang(张杰), Li-Ming Chen(陈黎明), and Ling-An Wu(吴令安). Chin. Phys. B, 2021, 30(6): 064202.
[12] 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.
[13] Accurate Deep Potential model for the Al-Cu-Mg alloy in the full concentration space
Wanrun Jiang(姜万润), Yuzhi Zhang(张与之), Linfeng Zhang(张林峰), and Han Wang(王涵). Chin. Phys. B, 2021, 30(5): 050706.
[14] Handwritten digit recognition based on ghost imaging with deep learning
Xing He(何行), Sheng-Mei Zhao(赵生妹), and Le Wang(王乐). Chin. Phys. B, 2021, 30(5): 054201.
[15] Variation of electron density in spectral broadening process in solid thin plates at 400 nm
Si-Yuan Xu(许思源), Yi-Tan Gao(高亦谈), Xiao-Xian Zhu(朱孝先), Kun Zhao(赵昆), Jiang-Feng Zhu(朱江峰), and Zhi-Yi Wei(魏志义). Chin. Phys. B, 2021, 30(10): 104205.
No Suggested Reading articles found!