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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

October 22, 2015 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Jalal Shatah (New York University, Courant Institute)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • NLS equation

  • non-linear PDE

  • dispersive PDEs

  • asymptotic behavior

  • resonance effects

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14381
Abstract

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.

 
Supplements
24942?type=thumb Shatah_Notes 597 KB application/pdf Download
Video/Audio Files

14381

H.264 Video 14381.mp4 317 MB video/mp4 rtsp://videos.msri.org/data/000/024/616/original/14381.mp4 Download
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