WKB analysis of non-elliptic nonlinear Schrodinger equations

Rémi Carles (1) , Clément Gallo (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Rémi Carles, Clément Gallo. WKB analysis of non-elliptic nonlinear Schrodinger equations. Communications in Contemporary Mathematics, 2020, 22 (6), pp.1950045. ⟨10.1142/S0219199719500457⟩. ⟨hal-01921759⟩