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WKB analysis of non-elliptic nonlinear Schrodinger equations
Journal article   Open access   Peer reviewed

WKB analysis of non-elliptic nonlinear Schrodinger equations

Rémi Carles and Clément Gallo
Communications in Contemporary Mathematics, Vol.22(6)
09/2020

Abstract

We justify the WKB analysis for generalized nonlinear Schrödinger 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.
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