A Riemann–Hilbert Problem Approach to Infinite Gap Hill's Operators and the Korteweg–de Vries Equation

DOI10.1093/imrn/rnz156zbMath1483.35145arXiv1810.07818OpenAlexW2988245797MaRDI QIDQ5005247

Patrik V. Nabelek, Kenneth T.-R. McLaughlin

Publication date: 9 August 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.07818

zbMATH Keywords

Riemann-Hilbert problemSchrödinger equationKorteweg-de Vries equationinverse spectral theoryHill's equationBloch-Floquet solutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Spectral theory and eigenvalue problems for partial differential equations (35P99) 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) Soliton solutions (35C08) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (4)

The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions ⋮ A Riemann-Hilbert method to algebro-geometric solutions of the Korteweg-de Vries equation ⋮ Computation of large-genus solutions of the Korteweg-de Vries equation ⋮ Elliptic finite-band potentials of a non-self-adjoint Dirac operator

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