The nonlinear Schrödinger equation with forcing involving products of eigenfunctions

DOI10.46298/ocnmp.9809zbMATH Open1545.35176MaRDI QIDQ6579362

Anouchah Latifi, A. S. Fokas

Publication date: 25 July 2024

Published in: Open Communications in Nonlinear Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Riemann-Hilbert problemnonlinear Schrödinger equation

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) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Riemann-Hilbert problems in context of PDEs (35Q15) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Unnamed Item
• Self-consistent sources for integrable equations via deformations of binary Darboux transformations
• The Davey-Stewartson equation with sources derived from nonlinear variable separation method
• Construction of higher-dimensional nonlinear integrable systems and of their solutions
• Linear integral transformations and hierarchies of integrable nonlinear evolution equations
• Integrability of linear and nonlinear evolution equations and the associated nonlinear Fourier transforms
• The dressing method and nonlocal Riemann-Hilbert problems
• An extension of integrable equations
• Integration of the Korteweg-de Vries equation with a source
• Solution of an initial-boundary value problem for coupled nonlinear waves
• The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources
• Integrable Rosochatius deformations of higher-order constrained flows and the soliton hierarchy with self-consistent sources
• The Degasperis–Procesi equation with self-consistent sources
• Ishimori-I equation with self-consistent sources
• Nonlinear resonant scattering and plasma instability: an integrable model
• Integration of the nonlinear Schrodinger equation with a source
• A unified transform method for solving linear and certain nonlinear PDEs
• The solutions of the NLS equations with self-consistent sources
• Negaton and positon solutions of the soliton equation with self-consistent sources
• The Linearization of the Initial-Boundary Value Problem of the Nonlinear Schrödinger Equation
• The nonlinear Schrödinger equation on the half-line
• Bäcklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources
• On the Toda lattice equation with self-consistent sources
• Darboux transformation and exact solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials
• The direct linearisation approach to hierarchies of integrable PDEs in 2 + 1 dimensions: I. Lattice equations and the differential-difference hierarchies

Related Items (1)

Resonance in oscillators with nonlinearity manifested at intermediate amplitudes

This page was built for publication: The nonlinear Schrödinger equation with forcing involving products of eigenfunctions