Perturbative approach to the interaction of solitons in quadratic nonlinear media

Abstract

We investigate the interaction between one-dimensional bright solitary waves in quadratic nonlinear media. We use a perturbational approach via collective coordinates to reduce the full evolution equations to a set of coupled ordinary differential equations which provides a simple qualitative picture of the soliton interactions. We use the scheme to calculate the collision distance between equal amplitude solitons and compare the results with the outcome of direct numerical solution of the evolution equations. A good agreement is found.