WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity

Rémi Carles (1) , Clément Gallo (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

We consider the semi-classical limit of nonlinear Schrodinger equations in the presence of both a polynomial nonlinearity and the derivative in space of a polynomial nonlinearity. By working in a class of analytic initial data, we do not have to assume any hyperbolic structure on the (limiting) phase/amplitude system. The solution, its approximation, and the error estimates are considered in time dependent analytic regularity.

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

Rémi Carles, Clément Gallo. WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity. Mathematical Models and Methods in Applied Sciences, 2017, 27 (9), pp.1727-1742. ⟨10.1142/S0218202517500300⟩. ⟨hal-01415010⟩