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

By Dmitry E. Pelinovsky, Yusuke Shimabukuro. 2016

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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 $H^2(\mathbb{R}) \cap H^{1,1}(\mathbb{R})$ 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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f3a707e96becb982d47fc9b7f0ed12691931bed2