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Existence of global solutions to the derivative NLS equation with the inverse scattering transform method (1602.02118v1)
Published 5 Feb 2016 in math.AP
Abstract: We address existence of global solutions to the derivative nonlinear Schr\"{o}dinger (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 $H2(\mathbb{R}) \cap H{1,1}(\mathbb{R})$ 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.