Vector NLS solitons interacting with a boundary*

Abstract

Abstract We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.