Vector NLS solitons interacting with a boundary

TL;DR

This paper develops multi-soliton solutions for the vector nonlinear Schrödinger equation on a half-line with specific boundary conditions, revealing boundary-bound solitons and component tuning effects.

Contribution

It introduces a dressing method to construct multi-soliton solutions satisfying integrable boundary conditions for the vector NLS equation.

Findings

Boundary-bound solitons under Robin BCs

Boundary acts as a polarizer for vector components

Explicit multi-soliton solutions derived

Abstract

We construct multi-soliton solutions of the n-component vector nonlinear Schr\"odinger 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 approach of dressing the integrable BCs: soliton solutions are generated in 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.