Nonuniqueness of weak solutions of the nonlinear Schroedinger equation
arXiv:math/0503366
Abstract
Generalized solutions of the Cauchy problem for the one-dimensional periodic nonlinear Schrödinger 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.
13 pages