The large box limit of nonlinear Schrodinger equations in weakly nonlinear regime
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: MSRI: Simons Auditorium
35Q55 - NLS-like equations (nonlinear Schrödinger) [See also 37K10]
35R15 - Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]
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.
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