International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 375-394
doi:10.1155/S0161171201011450

On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation

Abstract

We consider the Cauchy problem periodic in the spatial variable for the usual cubic nonlinear Schrödinger equation and construct an infinite sequence of invariant measures associated with higher conservation laws for dynamical systems generated by this problem on appropriate phase spaces. In addition, we obtain sufficient conditions for the boundedness of the measures constructed.