Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term

We consider the Cauchy problem of the third order NLS with Raman scattering term under the periodic boundary condition.
It has been universally used among physicists as a mathematical model for the photonic crystal fiber oscillator.
I show the nonexistence of solutions for some initial data and the norm inflation of the data-solution map in Sobolev spaces.
This talk is based on the joint work with Nobu Kishimoto, RIMS, Kyoto University.