Higher dimensional solitary waves generated by second-harmonic generation in quadratic media

Schrodinger type soliton waves generated by second-harmonic generation in higher dimensional quadratic optical media are considered. The existence of ground state solutions for spatial dimension from two to five is proved, and the continuous dependence on the parameter and asymptotic behavior of ground state solutions are established. Multi-pulse solutions with certain symmetry are also obtained. In a bounded domain setting, global bifurcation diagram of multi-pulse solutions are shown by using new technique of double saddle-node bifurcation.