  We consider the ill-posedness and well-posedness of the Cauchy problem for
the third order NLS equation with Raman scattering term on the one dimensional
torus. It is regarded as a mathematical model for the photonic crystal fiber
oscillator. Regarding the ill-posedness, we show the nonexistence of solutions
in the Sobolev space and the norm inflation of the data-solution map under
slightly different conditions, respectively. We also prove the local unique
existence of solutions in the analytic function space.
