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<p>We study the existence of global solutions to the initial value problem for the integrable nonlocal derivative nonlinear Schrödinger equation in weighted Sobolev space <i>H</i><sup>2</sup>(ℝ) ∩ <i>H</i><sup>1,1</sup> (ℝ), under a reasonably small norm assumption on the initial data. The key to proving this result is to establish the bijectivity between the potential and the reflection coefficient by using the inverse scattering transform method in the form of the Riemann-Hilbert (RH) problem.</p>

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Existence of global solutions for the nonlocal derivative nonlinear Schrödinger equation by the inverse scattering transform method

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Yuan Li,
  • Engui Fan

摘要

We study the existence of global solutions to the initial value problem for the integrable nonlocal derivative nonlinear Schrödinger equation in weighted Sobolev space H2(ℝ) ∩ H1,1 (ℝ), under a reasonably small norm assumption on the initial data. The key to proving this result is to establish the bijectivity between the potential and the reflection coefficient by using the inverse scattering transform method in the form of the Riemann-Hilbert (RH) problem.