MULTIPLE SOLITARY WAVES DUE TO 2ND-HARMONIC GENERATION IN QUADRATIC MEDIA

A detailed mathematical analysis is undertaken of solitary-wave soluti ons of a system of coupled nonlinear Schrodinger equations describing second-harmonic generation in optical materials with chi((2)) nonlinea rity. The so-called bright-bright case is studied exclusively. The sys tem depends on a single dimensionless parameter a that includes both w ave and material properties. Using methods from the calculus of variat ions, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive a. Recently, bound states (mult ipulsed solitary waves) have been found numerically. Using numerical c ontinuation, the region of existence of these solutions is revealed to be alpha is an element of (0, 1), and the bifurcations occurring at t he two extremes of this interval are uncovered.