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Power series solution of a nonlinear Schroedinger equation

Michael Christ
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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 L^2. 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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Michael Christ. 2005-03-17. Power series solution of a nonlinear Schroedinger equation. https://arxiv.org/abs/math/0503368

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