Dv. Skryabin et Wj. Firth, INSTABILITIES OF HIGHER-ORDER PARAMETRIC SOLITONS - FILAMENTATION VERSUS COALESCENCE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(2), 1998, pp. 1252-1255
We investigate stability and dynamics of higher-order solitary waves i
n quadratic media, which have a central peak and one or more surroundi
ng rings. We show the existence of two qualitatively different behavio
rs. For positive phase mismatch the rings break up into filaments that
move radially to the initial ring. For sufficient negative mismatches
rings are found to coalesce with the central peak, forming a single o
scillating filament.