Séminaire: The 1D periodic Schrödinger equation with concentrated nonlinearity

The Schrödinger equation with concentrated nonlinearity is an effective model for a quantum gas with an impurity. Its nonlinearity consists of a Dirac delta multiplied by the standard power-type nonlinearity. In this talk, I will discuss some aspects of its well-posedness on a circle for regular initial conditions. The proof is based on an inviscid limit of the complex Ginzburg-Landau equation, and exploiting the Volterra integral equation structure that arises from the concentrated nature of the nonlinearity.

Based on joint work with Jinyeop Lee (University of Basel).