Cauchy matrix structure and solutions of the spin-1 Gross-Pitaevskii equations

DOI10.1016/j.cnsns.2023.107705OpenAlexW4388812607MaRDI QIDQ6189444

Unnamed Author, Da-jun Zhang

Publication date: 8 February 2024

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2023.107705

zbMATH Keywords

nonlinear Schrödinger equationGross-Pitaevskii equationBose-Einstein condensatenonlocal integrable systemCauchy matrix approach

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) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• The Sylvester equation and integrable equations: the Ablowitz-Kaup-Newell-Segur system
• Cauchy matrix type solutions for the nonlocal nonlinear Schrödinger equation
• Long-time asymptotics for the spin-1 Gross-Pitaevskii equation
• The Coupled Modified Korteweg-de Vries Equations
• Solutions to the modified Korteweg–de Vries equation
• Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach
• Structure of a quantized vortex in boson systems
• Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
• Nonlocal nonlinear Schrödinger equations and their soliton solutions
• Matter-Wave Solitons in an F=1 Spinor Bose–Einstein Condensate
• Darboux Transformations and Global Explicit Solutions for Nonlocal Davey–Stewartson I Equation
• The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation
• Integrable properties of the general coupled nonlinear Schrödinger equations
• Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy
• The Fokas–Lenells equations: Bilinear approach
• Cauchy matrix approach to the SU(2) self‐dual Yang–Mills equation

This page was built for publication: Cauchy matrix structure and solutions of the spin-1 Gross-Pitaevskii equations