Self-Similar Solutions for Nonlinear Schrödinger Equations

Abstract

In this paper we study self-similar solutions for nonlinear Schrödinger equations using a scaling technique and the partly contractive mapping method.We establish the small global well-posedness of the Cauchy problem for nonlinear Schrödinger equations in some non-reflexive Banach spaces which contain many homogeneous functions.This we do by establishing some a priori nonlinear estimates in Besov spaces, employing the mean difference characterization and multiplication in Besov spaces.These new global solutions to nonlinear Schrödinger equations with small data admit a class of self-similar solutions.Our results improve and extend the well-known results of Planchon [18], Cazenave and Weissler [4,5] and Ribaud and Youssfi [20].

Locations

• Methods and Applications of Analysis - View - PDF
• Project Euclid (Cornell University) - View - PDF