Invariant Measures for Infinite-Dimensional Dynamical Systems with Applications to a Nonlinear Schrödinger Equation

1996 ◽  
pp. 471-476
Author(s):  
P. E. Zhidkov
Keyword(s):  
Dynamical Systems ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Invariant Measures ◽  
Nonlinear Schrodinger Equation ◽  
Infinite Dimensional ◽  
Nonlinear Schrödinger ◽  
Infinite Dimensional Dynamical Systems

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

2001 ◽  
Vol 28 (7) ◽  
pp. 375-394 ◽  
Author(s):  
Peter E. Zhidkov
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Invariant Measures ◽  
Infinite Sequence ◽  
Sufficient Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
The Cauchy Problem ◽  
Cubic Nonlinear Schrödinger Equation

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.

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