Nonuniqueness of weak solutions of the nonlinear Schroedinger equation

Details Nonuniqueness of weak solutions of the nonlinear Schroedinger equation Nonuniqueness of weak solutions of the nonlinear Schroedinger equation

2005-03-17

arxiv.org/abs/math/0503366v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

Generalized solutions of the Cauchy problem for the one-dimensional periodic
nonlinear Schr\"odinger equation, with certain nonlinearities, are not unique.
For any $s<0$ there exist nonzero generalized solutions varying continuously in
the Sobolev space $H^s$, with identically vanishing initial data.

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