Dynamics on resonant clusters for the quintic non linear Schr\"odinger equation

TL;DR

This paper constructs solutions to the quintic nonlinear Schrödinger equation on a circle, focusing on initial conditions supported on multiple resonant clusters, advancing understanding of resonant dynamics in nonlinear wave equations.

Contribution

It extends previous work by explicitly constructing solutions supported on multiple resonant clusters for the quintic NLS on the circle.

Findings

Solutions supported on arbitrarily many resonant clusters are constructed.

The work builds on and extends prior research by Grébert and the second author.

Provides new insights into the resonant dynamics of the quintic NLS.

Abstract

We construct solutions to the quintic nonlinear Schr\"odinger equation on the circle with initial conditions supported on arbitrarily many different resonant clusters. This is a sequel of a work of Beno\^it Gr\'ebert and the second author.