PINN deep learning method for the Chen–Lee–Liu equation: Rogue wave on the periodic background

Wei Qi Peng; Jun Cai Pu; Yong Chen

doi:10.1016/j.cnsns.2021.106067

PINN deep learning method for the Chen–Lee–Liu equation: Rogue wave on the periodic background

Wei Qi Peng
, Jun Cai Pu
, Yong Chen^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

105 Scopus citations

Abstract

We consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen–Lee–Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks (PINNs) deep learning method is applied to research the data-driven rogue periodic wave, breather wave, soliton wave and periodic wave solutions of well-known Chen–Lee–Liu equation. Especially, the data-driven rogue periodic wave is learned for the first time to solve the partial differential equation. In addition, using image simulation, the relevant dynamical behaviors and error analysis for there solutions are presented. The numerical results indicate that the rogue periodic wave, breather wave, soliton wave and periodic wave solutions for Chen–Lee–Liu equation can be generated well by PINNs deep learning method.

Original language	English
Article number	106067
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	105
DOIs	https://doi.org/10.1016/j.cnsns.2021.106067
State	Published - Feb 2022

Keywords

Breather wave
Deep learning
Periodic wave
Physics-informed neural networks
Rogue periodic wave
Soliton wave
The Chen–Lee–Liu equation

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10.1016/j.cnsns.2021.106067

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@article{d785e413b1b04e43954dd8e6d8697437,

title = "PINN deep learning method for the Chen–Lee–Liu equation: Rogue wave on the periodic background",

abstract = "We consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen–Lee–Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks (PINNs) deep learning method is applied to research the data-driven rogue periodic wave, breather wave, soliton wave and periodic wave solutions of well-known Chen–Lee–Liu equation. Especially, the data-driven rogue periodic wave is learned for the first time to solve the partial differential equation. In addition, using image simulation, the relevant dynamical behaviors and error analysis for there solutions are presented. The numerical results indicate that the rogue periodic wave, breather wave, soliton wave and periodic wave solutions for Chen–Lee–Liu equation can be generated well by PINNs deep learning method.",

keywords = "Breather wave, Deep learning, Periodic wave, Physics-informed neural networks, Rogue periodic wave, Soliton wave, The Chen–Lee–Liu equation",

author = "Peng, \{Wei Qi\} and Pu, \{Jun Cai\} and Yong Chen",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

month = feb,

doi = "10.1016/j.cnsns.2021.106067",

language = "英语",

volume = "105",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - PINN deep learning method for the Chen–Lee–Liu equation

T2 - Rogue wave on the periodic background

AU - Peng, Wei Qi

AU - Pu, Jun Cai

AU - Chen, Yong

PY - 2022/2

Y1 - 2022/2

N2 - We consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen–Lee–Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks (PINNs) deep learning method is applied to research the data-driven rogue periodic wave, breather wave, soliton wave and periodic wave solutions of well-known Chen–Lee–Liu equation. Especially, the data-driven rogue periodic wave is learned for the first time to solve the partial differential equation. In addition, using image simulation, the relevant dynamical behaviors and error analysis for there solutions are presented. The numerical results indicate that the rogue periodic wave, breather wave, soliton wave and periodic wave solutions for Chen–Lee–Liu equation can be generated well by PINNs deep learning method.

AB - We consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen–Lee–Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks (PINNs) deep learning method is applied to research the data-driven rogue periodic wave, breather wave, soliton wave and periodic wave solutions of well-known Chen–Lee–Liu equation. Especially, the data-driven rogue periodic wave is learned for the first time to solve the partial differential equation. In addition, using image simulation, the relevant dynamical behaviors and error analysis for there solutions are presented. The numerical results indicate that the rogue periodic wave, breather wave, soliton wave and periodic wave solutions for Chen–Lee–Liu equation can be generated well by PINNs deep learning method.

KW - Breather wave

KW - Deep learning

KW - Periodic wave

KW - Physics-informed neural networks

KW - Rogue periodic wave

KW - Soliton wave

KW - The Chen–Lee–Liu equation

UR - https://www.scopus.com/pages/publications/85117183703

U2 - 10.1016/j.cnsns.2021.106067

DO - 10.1016/j.cnsns.2021.106067

M3 - 文章

AN - SCOPUS:85117183703

SN - 1007-5704

VL - 105

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 106067

ER -

PINN deep learning method for the Chen–Lee–Liu equation: Rogue wave on the periodic background

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Keywords

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