The large box limit of nonlinear Schrodinger equations in weakly nonlinear regime
Jalal Shatah (New York University, Courant Institute)
MSRI: Simons Auditorium
We study the long time dynamics of solutions to nonlinear Schrodinger equations with periodic boundary conditions as the length of the period becomes infinite. We isolate the effects of resonant interactions and derive new evolution equations whose dynamics approximate the long time dynamics of localized solutions. We will show that this approximation is valid on a long time scale determined by the size of the solution and the length of the period.