Solitons for the coupled matrix nonlinear Schrödinger-type equations and the related Schrödinger flow

DOI10.1515/MATH-2022-0600zbMath1530.37097OpenAlexW4383099952MaRDI QIDQ6083247

Xinjie Wan, Zehui Zhao, Shiping Zhong

Publication date: 31 October 2023

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/math-2022-0600

zbMATH Keywords

gauge equivalenceSchrödinger flowcomplex Grassmannianmatrix AKNS hierarchycoupled matrix NLS equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Soliton solutions (35C08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlocal general vector nonlinear Schrödinger equations: integrability, \(\mathcal{PT}\) symmetribility, and solutions
• The noncommutative KdV equation and its para-Kähler structure
• Vortex filament on symmetric Lie algebras and generalized bi-Schrödinger flows
• A note on the NLS and the Schrödinger flow of maps
• Nonlinear Schrödinger equations and simple Lie algebras
• Schrödinger flow of maps into symplectic manifolds
• Geometric realizations of Fordy-Kulish nonlinear Schrödinger systems.
• \(n\)-dimension central affine curve flows
• The Chern connection of a \((J^{2}=\pm1)\)-metric manifold of class \({\mathcal{G}}_{1}\)
• Schrödinger flows, binormal motion for curves and the second AKNS-hierarchies
• Darboux transforms for the \(\hat{B}_n^{(1)}\)-hierarchy
• On the vortex filament in 3-spaces and its generalizations
• Application of Riemann-Hilbert method to an extended coupled nonlinear Schrödinger equations
• Reflectionless solutions for square matrix NLS with vanishing boundary conditions
• Direct and inverse scattering for the matrix Schrödinger equation
• The complex 2-sphere in \(\mathbb{C}^3\) and Schrödinger flows
• Darboux transformations for the \(\hat{A}_{2n}^{(2)}\)-KdV hierarchy
• Dispersive Geometric Curve Flows
• Nonlinear Waves in Integrable and Nonintegrable Systems
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Bäcklund transformations and loop group actions
• Schrödinger maps
• Integrable Nonlocal Nonlinear Equations
• Bäcklund transformations for Gelfand–Dickey Flows, revisited
• Soliton interactions in the vector NLS equation
• Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations
• The geometric airy curve flow on $\mathbb{R}^n$
• Solitons for the Schrödinger flows on Hermitian symmetric spaces
• Completely integrable curve flows on adjoint orbits
• Vector NLS solitons interacting with a boundary*

This page was built for publication: Solitons for the coupled matrix nonlinear Schrödinger-type equations and the related Schrödinger flow