Soliton solutions of the nonlinear Schrödinger equation with defect conditions.

Motivated by a recent development in the derivation of soliton solutions for initial-boundary value problems via the dressing method, we reconsider solutions to the nonlinear Schrödinger (NLS) equation on two half-lines connected via integrable defect conditions. The dressing method to construct soliton solutions is applied, while preserving the spectral boundary constraint with a time-dependent defect matrix. Moreover, N-soliton solutions are explicitly constructed and it is proven that the solitons are transmitted through the defect independently of one another. [ABSTRACT FROM AUTHOR]