WKB analysis of non-elliptic nonlinear Schrodinger equations

Abstract

We justify the WKB analysis for generalized nonlinear Schr{ö}dinger equations (NLS), including the hyperbolic NLS and the Davey-Stewartson II system. Since the leading order system in this analysis is not hyperbolic, we work with analytic regularity, with a radius of analyticity decaying with time, in order to obtain better energy estimates. This provides qualitative information regarding equations for which global well-posedness in Sobolev spaces is widely open.

arXiv admin note: text overlap with arXiv:1612.04149

References in corpus (2)

• On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit II. Analytic regularity
• WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity