International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 375-394
On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, (Moscow Region), Russia
Received 21 January 2001; Revised 28 May 2001
Copyright © 2001 Peter E. Zhidkov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.