# Effective dynamics of the dispersive equations and the Hardy-Littlewood circle method

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Jalal Shatah , NYU
Fine Hall 314

The long-time behavior of small amplitude solutions to nonlinear dispersive equations on $\mathbb{R}^n$ is relatively well understood. However, the situation is markedly different when these equations are considered on a bounded domain. In this talk, we will consider nonlinear Schrodinger equations on rational tori and show how to derive limiting equations that govern the long-time dynamics of solutions. The derivation of the limiting equations and the proofs rely heavily on results from analytic number theory.