D.E. Pelinovsky and Y. Shimabukuro
Global existence in the derivative NLS equation
with the inverse scattering transform method
International Mathematics Research Notices, Vol. 2018, No. 18, 5663–5728 (2018)
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