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

Soliton, Breather and Rogue Wave Solutions for Solving the Nonlinear Schrödinger Equation Using a Deep Learning Method with Physical Constraints

(2021) Pu Jun-Cai et al.   Chinese Physics B

Solving localized wave solutions of the derivative nonlinear Schrödinger equation using an improved PINN method

(2021) Juncai Pu et al.   NONLINEAR DYNAMICS

Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN

(2021) Yin Fang et al.   NONLINEAR DYNAMICS

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

(2020) Ameya D. Jagtap et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Rogue waves for the Hirota equation on the Jacobi elliptic cn-function background

(2020) Xia Gao et al.   NONLINEAR DYNAMICS

A physics-constrained deep residual network for solving the sine-Gordon equation

(2020) Jun Li et al.   COMMUNICATIONS IN THEORETICAL PHYSICS

Breathers and rogue waves on the periodic background for the Gerdjikov-Ivanov equation for the Alfvén waves in an astrophysical plasma

(2019) Cui-Cui Ding et al.   CHAOS SOLITONS & FRACTALS

Characteristics of rogue waves on a periodic background for the Hirota equation

(2019) Wei-Qi Peng et al.   WAVE MOTION

Rogue periodic waves of the sine–Gordon equation

(2019) Ruomeng Li et al.   APPLIED MATHEMATICS LETTERS

Rogue periodic waves of the modified KdV equation

(2018) Jinbing Chen et al.   NONLINEARITY

A Riemann-Hilbert Approach to the Chen-Lee-Liu Equation on the Half Line

(2018) Ning Zhang et al.   Acta Mathematicae Applicatae Sinica-English Series

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Darboux Transformation of the Second-Type Derivative Nonlinear Schrödinger Equation

(2015) Yongshuai Zhang et al.   LETTERS IN MATHEMATICAL PHYSICS

Deep learning

(2015) Yann LeCun et al.   NATURE

Rogue waves and solitons on a cnoidal background

(2014) D.J. Kedziora et al.   European Physical Journal-Special Topics

Generalized Darboux transformation and localized waves in coupled Hirota equations

(2014) Xin Wang et al.   WAVE MOTION

Rogue waves in coupled Hirota systems

(2013) Shihua Chen et al.   PHYSICAL REVIEW E

Rogue wave management in an inhomogeneous Nonlinear Fibre with higher order effects

(2013) J.S. He et al.   JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS

Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions

(2012) Boling Guo et al.   PHYSICAL REVIEW E

Active Control of Rogue Waves for Stimulated Supercontinuum Generation

(2008) D. R. Solli et al.   PHYSICAL REVIEW LETTERS

Generation of short-lived large-amplitude magnetohydrodynamic pulses by dispersive focusing

(2008) V. Fedun et al.   PHYSICS LETTERS A