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arXiv · 1811.07597

WKB analysis of non-elliptic nonlinear Schrodinger equations

Rémi Carles·Clément Gallo
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Abstract

We justify the WKB analysis for generalized nonlinear Schr{\"o}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.

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Rémi Carles, Clément Gallo. 2018-11-19. WKB analysis of non-elliptic nonlinear Schrodinger equations. https://doi.org/10.1142/s0219199719500457

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