ncku-talk2024-02-22

Colloquium

DATE 2024-02-22　14:10-15:00

PLACE 數學系館 1F3174教室

SPEAKER Hayato Miyazaki 副教授（Faculty of Education, Kagawa University）

TITLE Modified 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.

Colloquium

DATE	2024-02-22　14:10-15:00

PLACE	數學系館 1F3174教室

SPEAKER	Hayato Miyazaki 副教授（Faculty of Education, Kagawa University）

TITLE	Modified 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.