Multiple Solitary Waves Due to Second-Harmonic Generation in Quadratic Media

A detailed mathematical analysis is undertaken of solitary-wave solutions of a system of coupled nonlinear Schrödinger equations describing second-harmonic generation in optical materials with χ(2) nonlinearity. The so-called bright-bright case is studied exclusively. The system depends on a single dimensionless parameter α that includes both wave and material properties. Using methods from the calculus of variations, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive α . Recently, bound states (multipulsed solitary waves) have been found numerically. Using numerical continuation, the region of existence of these solutions is revealed to be α∈ (0,1), and the bifurcations occurring at the two extremes of this interval are uncovered.