WKB analysis for nonlinear Schrodinger equations with potential

Preprint
Publisher Website
Google Scholar
  • 25 January 2006
Abstract
We justify the WKB analysis for the semiclassical nonlinear Schrodinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity.

This publication has 0 references indexed in Scilit: