Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method Academic Article uri icon

  •  
  • Overview
  •  
  • Research
  •  
  • Identity
  •  
  • Additional Document Info
  •  
  • View All
  •  

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

publication date

  • September 26, 2018