Multiple solitary waves due to second-harmonic generation in quadratic media (Q1277228)

The authors study the solitary-wave solutions of two coupled nonlinear Schrödinger equations describing second-harmonic generation in optical materials with quadratic nonlinearity only the case ``bright-bright'' is studied. The system depends on a single parameter \(\alpha\) that includes both wave and material properties. The main result is that at least one solitary wave exists for \(\alpha>0\). That is obtained by using methods from calculus of variations. Finally, the paper provides strong numerical evidence that there are infinitely many multipulsed solitary waves (bound states) for \(\alpha\in(0, 1)\) with bifurcations at the two extremes.