Power series solution of a nonlinear Schroedinger equation

2005/03/17 by Michael Christ, Christ, Michael · 2 citations
Mathematics · Physics and Astronomy · #35Q55 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #advanced mathematical theories #math.AP #math.CA #msc:35Q55

paper · pdf · doi:10.48550/arxiv.math/0503368

18 pages

arxiv created 2005/03/17 · openalex publication_date 2005/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schroedinger equation is shown to admit weak solutions for all initial data in certain function spaces wider than L². These solutions depend uniformly continuously on the initial data, in the norms considered. The solutions are constructed as sums of infinite series of multilinear operators applied to initial data; no fixed point argument or energy inequality are used. In a companion paper we have shown that weak solutions in these same function spaces are however not unique.

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