International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 375-394
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.