DATE2019-02-21 15:10-16:00


SPEAKERYoshio Tsutsumi 教授(京都大學

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

ABSTRACT We consider the ill-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It has been universally used among physicists as a mathematical model for the photonic crystal fiber oscillator (see, e.g., [1]). I show the nonexistence of solutions in the Sobolev space and the norm inflation of the data-solution map at the origin under slightly different conditions, respectively. Physicists sometimes propose models which have strong instability from a mathematical point of view. Equation (1) is such a kind of example and it is not very clear what role the mathematical ill-posedness plays in physics. I also talk about the local unique existence of solutions in the analytic function space. This talk is based on the joint work [2] with Nobu Kishimoto, RIMS, Kyoto University. References [1] G. Agrawal, Nonlinear Fiber Optics, 4th edition, Elsevier / Academic Press, Burlington, 2007. [2] N. Kishimoto and Y. Tsutsumi, Ill-posedness of the third order NLS equation with Raman scattering term, preprint, arXiv: 1706.09111v1 [math.AP]