Direct analysis of the bright-soliton collisions in the focusing vector nonlinear Schrödinger equation

The multi-component Wronskian representation of the bright N-soliton solution to the focusing vector nonlinear Schrödinger equation for certain optical fibers allows a direct algebraic method to study the collision behavior of N vector solitons with m components. In this letter, this method is used to analyze the two- and three-soliton collisions via symbolic computation. The phase-shift formulae induced by the vector-soliton collisions are given explicitly, and the parametric conditions are revealed for the amplitude preservation of all the soliton components in the collision. In addition, the generalized linear fractional transformations are also derived to directly describe the state change for each component of colliding solitons.