##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Zaher Hani

#### Georgia Tech

## Effective dynamics of nonlinear Schrodinger equations on large domains

##### Abstract:

While the long-time behavior of small amplitude solutions to nonlinear dispersive and wave equations on Euclidean spaces $(R^n)$ is relatively well-understood, the situation is marked different on bounded domains. Due to the absence of dispersive decay, a very rich set of dynamics can be witnessed even starting from arbitrary small initial data. In particular, the dynamics in this setting is characterized by out-of-equilibrium behavior, in the sense that solutions typically do not exhibit long-time stability near equilibrium configurations. This is even true for equations posed on very large domains (e.g. water waves on the ocean) where the equation exhibits very different behaviors at various time-scales. In this talk, we shall consider the nonlinear Schr\"odinger equation posed on a large box of size $L$. We will analyze the various dynamics exhibited by this equation when $L$ is very large

Host: Ioan Bejenaru

### October 11, 2016

### 10:00 AM

### AP&M 7321

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