D.E. Pelinovsky and Y. Shimabukuro

Global existence in the derivative NLS equation with the inverse scattering transform method


Abstract:
We address existence of global solutions of the derivative nonlinear Schrodinger (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 intersecting with H1,1, which is also Lipschitz continuous with respect to the initial data. Compared to the existing literature on the spectral problem for the DNLS equation, we transform the Riemann-Hilbert problem in the complex plane to the jump on the real line.

Keywords:
derivative NLS equation, global existence, inverse scattering transform, Kaup-Newell spectral problem, Riemann-Hilbert problem