WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity

TL;DR

This paper analyzes the semi-classical limit of generalized derivative nonlinear Schrödinger equations without assuming hyperbolicity, using analytic initial data to establish solution approximations and error estimates.

Contribution

It introduces a WKB analysis framework for these equations without hyperbolic assumptions, expanding the understanding of their semi-classical behavior.

Findings

Established solution existence and approximation in analytic regularity

Derived error estimates for the semi-classical limit

Extended analysis to equations with derivative nonlinearities

Abstract

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