D.E. Pelinovsky, A.V. Buryak, and Yu.S. Kivshar
Instabilities of solitons governed by
quadratic nonlinearities
Phys.Rev.Lett. 75, 591-595 (1995)
Abstract:
Stability of two-wave solitons supported by resonant parametric
interactions in a diffractive (or dispersive) optical quadratic
medium is investigated analytically and
numerically. It is found that the solitons can become unstable
when the phase matching between the fundamental and second
harmonics is not exactly satisfied. The
analytical criterion for the linear instability is presented,
and it is revealed that the instability leads to two possible
scenarios of the soliton dynamics, either
large-amplitude in-phase oscillations of two harmonics or
the soliton decay.