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Mathematical Physics Seminar

Knocking out teeth in one-dimensional periodic NLS

Nikos Pattakos - Karlsruhe Inst. of Technology 

Location:  Hill 705
Date & time: Thursday, 25 October 2018 at 2:00PM - 3:00PM

Abstract:  We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrodinger equation in one dimension with initial data u_{0} in H^{s}(R)+H^{r}(T), 0leq s leq r, where T is the one dimensional torus. In addition, we show that if u_{0} is in H^{s}(R)+H^{frac12+epsilon}(T), epsilon>0, frac16leq sleqfrac12, the solution is unique in H^{s}(R)+H^{frac12+epsilon}(T). 

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