N-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann–Hilbert method and PINN algorithm

A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions

(2022) Shuning Lin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Riemann–Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions

(2022) Jin-Jie Yang et al.   PHYSICA D-NONLINEAR PHENOMENA

Dynamic behaviors of general N-solitons for the nonlocal generalized nonlinear Schrödinger equation

(2021) Minmin Wang et al.   NONLINEAR DYNAMICS

The ∂̄-dressing method and soliton solutions for the three-component coupled Hirota equations

(2021) Zi-Yi Wang et al.   JOURNAL OF MATHEMATICAL PHYSICS

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

(2021) Juncai Pu et al.   NONLINEAR DYNAMICS

Nonlocal continuous Hirota equation: Darboux transformation and symmetry broken and unbroken soliton solutions

(2021) Na-Na Li et al.   NONLINEAR DYNAMICS

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

(2021) Wei-Qi Peng et al.   Communications in Nonlinear Science and Numerical Simulation

A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrödinger equation

(2021) Rui-Qi Wang et al.   Communications in Nonlinear Science and Numerical Simulation

Breathers and rogue waves on the double-periodic background for the reverse-space-time derivative nonlinear Schrödinger equation

(2021) Huijuan Zhou et al.   NONLINEAR DYNAMICS

Extreme superposition: Rogue waves of infinite order and the Painlevé-III hierarchy

(2020) Deniz Bilman et al.   DUKE MATHEMATICAL JOURNAL

Solitons and rogue waves of the quartic nonlinear Schrödinger equation by Riemann–Hilbert approach

(2020) Nan Liu et al.   NONLINEAR DYNAMICS

The regularity of the multiple higher‐order poles solitons of the NLS equation

(2020) Yongshuai Zhang et al.   STUDIES IN APPLIED MATHEMATICS

A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation

(2019) Deniz Bilman et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Riemann-Hilbert method for the Wadati-Konno-Ichikawa equation: N simple poles and one higher-order pole

(2019) Yongshuai Zhang et al.   PHYSICA D-NONLINEAR PHENOMENA

Integrable nonlocal Hirota equations

(2019) Julia Cen et al.   JOURNAL OF MATHEMATICAL PHYSICS

Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions

(2019) Guoqiang Zhang et al.   PHYSICA D-NONLINEAR PHENOMENA

The higher-order nonlinear Schrödinger equation with non-zero boundary conditions: Robust inverse scattering transform, breathers, and rogons

(2019) Shuyan Chen et al.   PHYSICS LETTERS A

Inverse scattering transformation for generalized nonlinear Schrödinger equation

(2019) Xiaoen Zhang et al.   APPLIED MATHEMATICS LETTERS

Riemann–Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrödinger equations

(2019) Wei-Qi Peng et al.   JOURNAL OF GEOMETRY AND PHYSICS

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

(2018) Mark J. Ablowitz et al.   JOURNAL OF MATHEMATICAL PHYSICS

Darboux Transformations and Global Explicit Solutions for Nonlocal Davey-Stewartson I Equation

(2018) Zi-Xiang Zhou   STUDIES IN APPLIED MATHEMATICS

Reverse Space-Time Nonlocal Sine-Gordon/Sinh-Gordon Equations with Nonzero Boundary Conditions

(2018) Mark J. Ablowitz et al.   STUDIES IN APPLIED MATHEMATICS

General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

(2018) Bao-Feng Feng et al.   NONLINEARITY

High-order soliton matrices for Sasa–Satsuma equation via local Riemann–Hilbert problem

(2018) Bo Yang et al.   NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

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

Soliton solutions of an integrable nonlocal modified Korteweg–de Vries equation through inverse scattering transform

(2017) Jia-Liang Ji et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Rational and Semirational Solutions of the Nonlocal Davey-Stewartson Equations

(2017) J. Rao et al.   STUDIES IN APPLIED MATHEMATICS

Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation

(2016) A S Fokas   NONLINEARITY

Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

(2016) Mark J Ablowitz et al.   NONLINEARITY

Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions

(2016) Gino Biondini et al.   PHYSICA D-NONLINEAR PHENOMENA

Integrable Nonlocal Nonlinear Equations

(2016) Mark J. Ablowitz et al.   STUDIES IN APPLIED MATHEMATICS

Riemann–Hilbert approach and N-soliton solutions for a generalized Sasa–Satsuma equation

(2016) Xianguo Geng et al.   WAVE MOTION

Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions

(2014) Gino Biondini et al.   JOURNAL OF MATHEMATICAL PHYSICS

Observation of PT phase transition in a simple mechanical system

(2013) Carl M. Bender et al.   AMERICAN JOURNAL OF PHYSICS

Integrable Nonlocal Nonlinear Schrödinger Equation

(2013) Mark J. Ablowitz et al.   PHYSICAL REVIEW LETTERS

Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation

(2012) Boling Guo et al.   JOURNAL OF MATHEMATICAL PHYSICS

Integrable properties of the general coupled nonlinear Schrödinger equations

(2010) Deng-Shan Wang et al.   JOURNAL OF MATHEMATICAL PHYSICS