D.E. Pelinovsky, Yu.S. Kivshar, and V.V. Afanasjev
Instability-induced dynamics of dark solitons
Phys.Rev.E 54, 2015-2032 (1996)
Abstract:
Nonlinear theory describing the instability-induced dynamics
of dark solitons in the generalized nonlinear Schrodinger
equation is presented. Equations for the evolution
of an unstable dark soliton, including its transformation
into a stable soliton, are derived using a multiscale asymptotic
technique valid near the soliton instability
threshold. Results of the asymptotic theory are applied to
analyze dark solitons in physically important models of
optical nonlinearities, including competing, saturable,
and transiting nonlinearities. It is shown that in all
these models dark solitons may become unstable, and two
general (bounded and unbounded) scenarios of the instability
development are investigated analytically. Results of
direct numerical simulations of the generalized nonlinear
Schrodinger equation are also presented, which confirm
predictions of the analytical approach and display main
features of the instability-induced dynamics of dark
solitons beyond the applicability limits of the multiscale
asymptotic theory.
Keywords:
NONLINEAR SCHRODINGER EQUATION, PHOTOVOLTAIC SPATIAL SOLITONS,
SEMICONDUCTOR-DOPED GLASSES, WAVE-GUIDES, DEFOCUSING MEDIA,
REFRACTIVE INDEX, PROPAGATION, FIBERS