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Existence of global solutions for the nonlocal derivation nonlinear Schr\"{o}dinger equation by the inverse scattering transform method

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arxiv 2307.15837 v1 pith:SYSYLXRU submitted 2023-07-28 math.AP math-phmath.MP

Yuan Li , Xinhan Liu , Engui Fan This is my paper · ORCID
classification math.APmath-phmath.MP
keywords dingerequationexistenceglobalinversemathbbmethodnonlinear
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abstract

We address the existence of global solutions to the initial value problem for the integrable nonlocal derivative nonlinear Schr\"{o}dinger equation in weighted Sobolev space $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$. The key to prove this result is to establish a bijectivity between potential and reflection coefficient by using the inverse scattering transform method in the form of the Riemann-Hilbert problem.

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Cited by 1 Pith paper

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  1. On the global well-posedness for the nonlocal Fokas-Lenells equation with the weighted Sobolev initial data on the line

    nlin.SI 2026-07 reject novelty 6.0 of 10

    Claims global well-posedness for the reverse space-time nonlocal Fokas–Lenells equation under a small effective-potential condition, but the key spectral-decay step is derived circularly from the target equation.

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