Global conservative solutions of the nonlocal NLS equation beyond blow-up
DOI10.3934/dcds.2022173zbMath1515.35257arXiv2209.11261OpenAlexW4313208577MaRDI QIDQ6043610
Yan Rybalko, Dimitry Shepelsky
Publication date: 23 May 2023
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2209.11261
Riemann-Hilbert problemglobal well-posednessinverse scattering transform methodnonlocal nonlinear Schrödinger equationcontinuation beyond blow-up
Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Continuation and prolongation of solutions to PDEs (35B60) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15) Blow-up in context of PDEs (35B44) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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