DATE2024-02-22 14:10-15:00

PLACE數學系館 1F3174教室

SPEAKERHayato Miyazaki 副教授(Faculty of Education, Kagawa University

TITLEModified Scattering Operator for Nonlinear Schr\"odinger Equations with a Time-Decaying Harmonic Potential

ABSTRACT We consider nonlinear Schr\"odinger 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.