Interaction Between Two Nonlinear Schrödinger Solitons

The interaction between nonlinear Schrödinger solitons is derived by the least action principle approach as a potential function of the soliton's separation and their initial relative phase, which shows clearly how the solitons interact with each other. Two solitons with the same initial phase always attract each other, while those of opposite phase repel. The method developed in this paper can be extended to deal with interaction between solitons of other nonlinear equations.