Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium

Y Shen, B Tian, TY Zhou, CD Cheng - Chaos, Solitons & Fractals, 2023 - Elsevier
Investigations on nonlinear optics are active, with the applications in the modulators, fiber
lasers, optical sensors, etc. In this paper, we focus our attention on a system for the ultra …

Dynamic analysis on optical pulses via modified PINNs: Soliton solutions, rogue waves and parameter discovery of the CQ-NLSE

YH Yin, X Lü - Communications in Nonlinear Science and Numerical …, 2023 - Elsevier
Under investigation in this paper is the cubic–quintic nonlinear Schrödinger equation, which
describes the propagation of optical on resonant-frequency fields in the inhomogeneous …

Exotic vector freak waves in the nonlocal nonlinear Schrödinger equation

XB Wang, SF Tian - Physica D: Nonlinear Phenomena, 2022 - Elsevier
In this paper, general higher-order freak wave solutions of the nonlocal nonlinear
Schrödinger equation (NLSE) with parity-time symmetric can be calculated theoretically via …

Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints

JC Pu, J Li, Y Chen - Chinese Physics B, 2021 - iopscience.iop.org
The nonlinear Schrödinger equation is a classical integrable equation which contains plenty
of significant properties and occurs in many physical areas. However, due to the difficulty of …

Dynamics of rogue waves in the Davey–Stewartson II equation

Y Ohta, J Yang - Journal of Physics A: Mathematical and …, 2013 - iopscience.iop.org
General rogue waves in the Davey–Stewartson (DS) II equation are derived by the bilinear
method, and the solutions are given through determinants. It is shown that the simplest …

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

J Pu, J Li, Y Chen - Nonlinear Dynamics, 2021 - Springer
The solving of the derivative nonlinear Schrödinger equation (DNLS) has attracted
considerable attention in theoretical analysis and physical applications. Based on the …

[HTML][HTML] Inverse scattering transformation for generalized nonlinear Schrödinger equation

X Zhang, Y Chen - Applied Mathematics Letters, 2019 - Elsevier
Based on the robust inverse scattering method, the high-order rogue wave of generalized
nonlinear Schrödinger equation with nonzero boundary is given. Using this method, we only …

Transformations between nonlocal and local integrable equations

B Yang, J Yang - Studies in applied mathematics, 2018 - Wiley Online Library
Recently, a number of nonlocal integrable equations, such as the‐symmetric nonlinear
Schrödinger (NLS) equation and‐symmetric Davey–Stewartson equations, were proposed …

Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential

XY Wen, Z Yan, Y Yang - Chaos: An Interdisciplinary Journal of …, 2016 - pubs.aip.org
The integrable nonlocal nonlinear Schrödinger equation with the self-induced parity-time-
symmetric potential [MJ Ablowitz and ZH Musslimani, Phys. Rev. Lett. 110, 064105 (2013)] is …

[HTML][HTML] Lump and interaction solutions to the (2+ 1)-dimensional Burgers equation

H Wang - Applied Mathematics Letters, 2018 - Elsevier
Based on the Hirota bilinear method, the lump solution of a (2+ 1)-dimensional Burgers
equations is presented through symbolic computation with Maple, which is rationally …