Home /  Model problems in fluid dynamics: Stability of the cubic nonlinear Schrodinger equation on the Irrational Torus

Seminar

Model problems in fluid dynamics: Stability of the cubic nonlinear Schrodinger equation on the Irrational Torus April 05, 2021 (08:30 AM PDT - 09:30 AM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Bobby Wilson (University of Washington)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Stability of the Cubic Nonlinear Schrodinger Equation on the Irrational Torus
Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:

A characteristic of the defocusing cubic nonlinear Schrodinger equation (NLSE), when defined so that the space variable is the multi-dimensional square torus, is that  there exist solutions that start with arbitrarily small norms Sobolev norms and  evolve to develop  arbitrarily large modes at later times; this phenomenon is recognized as a weak  energy transfer to high modes for the NLSE. In this talk we will discuss research and numerical simulations that  show that, when the system is considered on an irrational torus, energy transfer is diminished. This is joint work with Gigliola Staffilani and Yulin Pan.

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Stability of the Cubic Nonlinear Schrodinger Equation on the Irrational Torus