PDE Seminar (2017/1/6): On the resonance energy transfer for some nonlinear Schr\”odinger equations on the torus, Hideo Takaoka (Hokkaido University)

2017-1-6 16:30 - 2017-1-6 17:30
Faculty of Science Building #3, Room 309
Hideo Takaoka (Hokkaido University)
We study the nonlinear energy exchanges between the Fourier modes for nonlinear Schr\"odinger equations with periodic boundary condition. Transfer of energy basically occurs at resonant modulus such as tuning forks vibrating at the same frequency. We introduce a static toy model of the derivative nonlinear Schr\"odinger equations and prove the existence of solution which periodically exchanges energy for certain time interval. Furthermore, we discuss the problem in the large space-periodic setting and about related topics.