Interaction between two dark solitons in optical fibers

The interaction between two dark solitons of nonlinear Schrodinger equation is derived with the variational principle approach. The interaction as a function of the soliton's separation Δ and their initial relative phase θ shows that the interaction decreased exponentially as Δ raise, and that two solitons repulse with each other when θπ/2.Analysis conforms to numerical calculation and it has also proved the validity of the existed theory.