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Instabilities of higher-order parametric solitons: Filamentation versus coalescence

Skryabin, Dmitry V. and Firth, William J. (1998) Instabilities of higher-order parametric solitons: Filamentation versus coalescence. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 58 (2). R1252 -R1255. ISSN 1063-651X

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We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show the existence of two qualitatively different behaviors. 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 oscillating filament.