The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions

DOI10.1007/s11005-021-01356-7zbMath1466.35325arXiv2104.04857OpenAlexW3181324063MaRDI QIDQ829966

Bernard Deconinck, Jonatan Lenells, Athanassios S. Fokas

Publication date: 7 May 2021

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.04857

zbMATH Keywords

Riemann-Hilbert problemperiodic solutioninverse scatteringFokas methodintegrable evolution equationlinearizable boundary conditionfinite-gap solutionunified transform method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Periodic solutions to PDEs (35B10) Boundary value problems for nonlinear higher-order PDEs (35G30) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (3)

The unified transform method to the high-order nonlinear Schrödinger equation with periodic initial condition ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ Phase computation for the finite-genus solutions to the focusing nonlinear Schrödinger equation using convolutional neural networks

Cites Work

• Unnamed Item
• Unnamed Item
• Computational approach to Riemann surfaces.
• The spectrum of Hill's equation
• Hyperelliptic Riemann surfaces of infinite genus and solutions of the KdV equation
• The nonlinear Schrödinger equation on the interval
• Method for Solving the Korteweg-deVries Equation
• A unified transform method for solving linear and certain nonlinear PDEs
• Riemann Surfaces of Infinite Genus
• A Riemann–Hilbert Problem Approach to Infinite Gap Hill's Operators and the Korteweg–de Vries Equation
• 30 years of finite-gap integration theory

This page was built for publication: The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions