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

Peter E. Zhidkov

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.