GROWTH AND OSCILLATIONS OF SOLUTIONS OF NONLINEAR SCHRODINGER-EQUATION

We study the nonlinear Schrodinger equation in an n-cube, n = 1,2,3, u nder Dirichlet boundary conditions, treating it as a dynamical system in a function space formed by sufficiently smooth functions of x. We s how that this space contains a distinguished small subset U which is a recursion subset for the dynamical system and describe the dynamics o f the equation in terms of the trajectory's recurrence to U. We use th is description to estimate from below the space- and time-space oscill ations of solutions in terms of a quantity, similar to the Reynolds nu mber of classical hydrodynamics.