Dark–dark and dark–bright soliton interactions in the two-component defocusing nonlinear Schrödinger equation

Abstract

We use the Inverse Scattering Transform machinery to construct multisoliton solutions to the 2-component defocusing nonlinear Schrödinger equation. Such solutions include dark–dark solitons, which have dark solitonic behaviour in both components, as well as dark–bright soliton solutions, with one dark and one bright component. We then derive the explicit expressions of two soliton solutions for all possible cases: two dark–dark solitons, two dark–bright solitons, and one dark–dark and one dark–bright soliton. Finally, we determine the long-time asymptotic behaviours of these solutions, which allows us to obtain explicit expressions for the shifts in the phases and in the soliton centers due to the interactions.

Keywords:

• inverse scattering transform
• nonlinear schrödinger systems
• solitons

AMS Subject Classifications::

• 37K15
• 35K61

Acknowledgements

This work was partially supported by the National Science Foundation under Grant No. DMS-1009248, by INFN, and PRIN 2008 ‘Geometrical methods in the theory of nonlinear integrable systems’.