Existence of dynamics for a 1D NLS equation perturbed with a generalized point defect

  title={Existence of dynamics for a 1D NLS equation perturbed with a generalized point defect},
  author={Riccardo Adami and Diego Noja},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • R. AdamiD. Noja
  • Published 25 November 2009
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
In the present paper we study the well-posedness for the one-dimensional cubic NLS perturbed by a generic point interaction. Point interactions are described as the 4-parameter family of self-adjoint extensions of the symmetric 1D Laplacian defined on the regular functions vanishing at a point, and in the present context can be interpreted as localized defects interacting with the NLS field. A previously treated special case is given by an NLS equation with a δ defect which we generalize and… 

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