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We consider the ill-posedness and well-posedness of the Cauchy problem forthe third order NLS equation with Raman scattering term on the one dimensionaltorus. It is regarded as a mathematical model for the photonic crystal fiberoscillator. Regarding the ill-posedness, we show the nonexistence of solutionsin the Sobolev space and the norm inflation of the data-solution map underslightly different conditions, respectively. We also prove the local uniqueexistence of solutions in the analytic function space.

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