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Bobby Wilson: Stability of the cubic nonlinear Schrodinger equation on the irrational torus

Submitted by Jorge Cisneros on February 4, 2021 - 11:00am
Bobby Wilson

Speaker: Bobby Wilson, UW

Date: February 4, 2021

Title: Stability of the cubic nonlinear Schrodinger equation on the irrational torus

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 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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