Title: Modified scattering operator for nonlinear Schrödinger equations with a time-decaying harmonic potential

Speaker: Dr Hayato Miyazaki, Kagawa University

Abstract: We consider nonlinear Schrödinger equations with a time-decaying harmonic potential. The nonlinearity is gauge-invariant of the long-range critical order. Kawamoto and Muramatsu show that the equation admits a nontrivial solution that behaves like a free solution with a logarithmic phase correction in the frameworks of both the final state problem and the initial value problem. Also, in the equation without the potential, Hayashi and Naumkin establish the existence of a modified scattering operator. In this talk, we construct a modified scattering operator for our equation by utilizing a generator of the Galilean transformation.

This talk is based on a joint work with Masaki Kawamoto (Okayama University).

The link to the slides of the talk:

https://www.nottingham.edu.cn/en/Science-Engineering/documents/NottinghamNingbo2405-Slide.pdf

This is the link to the recorded talk:

https://video.nottingham.edu.cn/Panopto/Pages/Viewer.aspx?id=69f66e5d-7897-48a4-9ee7-b16f00306d79