# On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schr\"odinger equations

## TL;DR

This paper proves that Gaussian measures remain quasi-invariant when evolved under the flow of one-dimensional cubic fractional nonlinear Schrödinger equations, under certain regularity conditions.

## Contribution

It establishes the quasi-invariance of Gaussian measures for fractional NLS equations, extending understanding of measure transport in infinite-dimensional Hamiltonian systems.

## Key findings

- Gaussian measures are quasi-invariant under fractional NLS flow
- Results hold under specific regularity conditions
- Advances measure transport theory in nonlinear dispersive PDEs

## Abstract

Under certain regularity conditions, we establish quasi-invariance of Gaussian measures on periodic functions under the flow of cubic fractional nonlinear Schr\"{o}dinger equations on the one-dimensional torus.