Global Existence for the Derivative Nonlinear Schrödinger Equation with Arbitrary Spectral Singularities

Abstract

We show that the derivative nonlinear Schrödinger (DNLS) equation is globally well-posed in the weighted Sobolev space $H^{2,2}(\mathbb{R})$. Our result exploits the complete integrability of DNLS and removes certain spectral conditions on the initial data, thanks to Xin Zhou's analysis on spectral singularities in the context of inverse scattering.

arXiv comment40 pages, 10 figures, revised per referee comments

References in corpus (4)

• Soliton Resolution for the Derivative Nonlinear Schrödinger Equation
• Global well-posedness on the derivative nonlinear Schrödinger equation revisited
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• $L^2$-Sobolev space bijectivity of the inverse scattering of a $3\times 3$ AKNS system

Cited by in corpus (7)

• On the well-posedness problem for the derivative nonlinear Schrödinger equation
• Potential well theory for the derivative nonlinear Schrödinger equation
• Stability of algebraic solitons for nonlinear Schrödinger equations of derivative type: variational approach
• Numerical inverse scattering transform for the derivative nonlinear Schrodinger equation
• The stability of degenerate solitons for derivative nonlinear Schrodinger equations
• Instability of degenerate solitons for nonlinear Schrödinger equations with derivative
• Nowhere continuity of the flow map of an integrable derivative nonlinear Schrödinger system on the torus