Generalized gauge transformation approach to construct dark solitons of coupled nonlinear Schrodinger type equations

We harness the freedom in the celebrated gauge transformation approach to generate dark solitons of coupled nonlinear Schr\"odinger (NLS) type equations. The new approach which is purely algebraic could prove to be very useful, particularly in the construction of vector dark solitons in the fields of nonlinear optics, plasma physics and Bose-Einstein condensates. We have employed this algebraic method to coupled Gross- Pitaevskii (GP) and NLS equations and obtained dark solitons.