SIMULTANEOUS SOLITARY-WAVE SOLUTIONS IN A NONLINEAR PARAMETRIC WAVE-GUIDE

We introduce a simple topological classification for the solitary-wave solutions of the coupled equations describing chi((2)) parametric wav eguides. Both temporal and spatial cases are studied. Simultaneous sol itary-wave solutions at two different frequencies, which we term ''sim ultons,'' are shown to exist using topological arguments. In each case , families or general one-parameter simultons are given numerically. E ach family consists of both fundamental and higher-order simultons of a topological or nontopological nature. There are several possible way s to combine dispersions at different frequencies. Thus there are more possible ways of maintaining temporal simultons in 1+1 space-time tha n for purely spatial simultons in two space dimensions.