A nonlinear Schrödinger equation with two symmetric point interactions in one dimension

Hynek Kovařík, Andrea Sacchetti
2010 Journal of Physics A: Mathematical and Theoretical  
We consider a time-dependent one-dimensional nonlinear Schroedinger equation with a symmetric potential double well represented by two delta interactions. Among our results we give an explicit formula for the integral kernel of the unitary semigroup associated with the linear part of the Hamiltonian. Then we establish the corresponding Strichartz-type estimate and we prove local existence and uniqueness of the solution to the original nonlinear problem.
doi:10.1088/1751-8113/43/15/155205 fatcat:4vgo7gthj5antabenfti7egsga