Methods and Applications of Analysis

Self-Similar Solutions for Nonlinear Schrodinger Equations

Changxing Miao, Bo Zhang, and Xiaoyi Zhang

Abstract

In this paper we study self-similar solutions for nonlinear Schrodinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrodinger 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 Schrodinger 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].

Article information

Source
Methods Appl. Anal., Volume 10, Number 1 (2003), 119-136.

Dates
First available in Project Euclid: 16 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.maa/1118943105

Mathematical Reviews number (MathSciNet)
MR2014165

Zentralblatt MATH identifier
1076.35118

Citation

Miao, Changxing; Zhang, Bo; Zhang, Xiaoyi. Self-Similar Solutions for Nonlinear Schrodinger Equations. Methods Appl. Anal. 10 (2003), no. 1, 119--136. https://projecteuclid.org/euclid.maa/1118943105


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