Existence of global solutions to the derivative NLS equation with the inverse scattering transform method

Abstract

We address existence of global solutions to the derivative nonlinear Schrödinger (DNLS) equation without the small-norm assumption. By using the inverse scattering transform method without eigenvalues and resonances, we construct a unique global solution in $H^2(\mathbb{R})\cap H^{1,1}(\mathbb{R})$ which is also Lipschitz continuous with respect to the initial data. Compared to the existing literature on the spectral problem for the DNLS equation, the corresponding Riemann--Hilbert problem is defined in the complex plane with the jump on the real line.

References in corpus (1)

• Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering

Cited by in corpus (5)

• Stability of multi-solitons for the derivative nonlinear Schr{ö}dinger equation
• Stability of the traveling waves for the derivative Schrödinger equation in the energy space
• Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering
• Local structure of singular profiles for a Derivative Nonlinear Schrödinger Equation
• Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in $H^{\frac{1}{2}}$