Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations

We study the transport property of Gaussian measures on Sobolev spaces periodic functions under dynamics one-dimensional cubic fractional nonlinear Schrödinger equation. For case second-order dispersion or greater, we establish an optimal regularity result for quasi-invariance these measures, following approach by Debussche and Tsutsumi (2021). Moreover, obtain explicit formula Radon-Nikodym derivative and, as a corollary, two-point function arising in wave turbulence theory. also improved results weakly dispersive case, extending those first author Trenberth (2019). Our proof combines introduced Planchon, Tzvetkov Visciglia (2020) that