Zaher Hani Seminar: A Continuum Large Box Limit for the Cubic Nonlinear Schrödinger Equation

Analysis & Applied Math Seminar 2013-03-21 Speaker: Zaher Hani Institution: New York University Abstract: Inspired by the general paradigm of weak turbulence theory, we consider the 2D cubic nonlinear Schrödinger equation on a box of size L with periodic boundary conditions. In an appropriate “large box regime” (L very large), we derive a continuum equation on ℝ2 that governs the dynamics of the discrete frequency modes over nonlinear time scales. This equation turns out to satisfy many surprising symmetries and conservation laws, as well as several families of explicit solutions.
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