Nonlinear Schroedinger equation with two symmetric point interactions in one dimension

Abstract

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.

References in corpus (5)

• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Fast soliton scattering by delta impurities
• Soliton splitting by external delta potentials
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Cited by in corpus (4)

• Bifurcation and stability for Nonlinear Schroedinger equations with double well potential in the semiclassical limit
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions
• Quantum diffusion in the Kronig-Penney model
• The Dispersion property for Schrödinger equations