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

Zhidkov, Peter E.

doi:https://doi.org/10.1155/S0161171201011450

International Journal of Mathematics and Mathematical Sciences

On this page

Abstract Copyright Related Articles

Open Access

Volume 28 | Article ID 320424 | https://doi.org/10.1155/S0161171201011450

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

Peter E. Zhidkov¹

Received21 Jan 2001

Revised28 May 2001

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.

Copyright

Copyright © 2001 Hindawi Publishing Corporation. 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.

PDF Download Citation Order printed copies

Views

150

Downloads

814

Citations