D.E. Pelinovsky, V.V. Afanasjev, and V.V. Kivshar
Nonlinear theory of oscillating, decaying, and collapsing solitons
in the generalized nonlinear Schrodinger equation
Phys.Rev.E. 53, 1940-1953 (1996)
Abstract:
A nonlinear theory describing the long-term dynamics of
unstable solitons in the generalized nonlinear Schrodinger
(NLS) equation is proposed. An analytical model for
the instability-induced evolution of the soliton parameters
is derived in the framework of the perturbation theory,
which is valid near the threshold of the soliton
instability. As a particular example, we analyze solitons
in the NLS-type equation with two power-law nonlinearities.
For weakly subcritical perturbations, the
analytical model reduces to a second-order equation with
quadratic nonlinearity that can describe, depending on
the initial conditions and the model parameters, three
possible scenarios of the longterm soliton evolution:
(i) periodic oscillations of the soliton amplitude near
a stable state, (ii) soliton decay into dispersive waves, and (iii)
soliton collapse. We also present the results of numerical
simulations that confirm excellently the predictions of
our analytical theory.
Keywords:
BISTABLE SOLITONS, PULSE-PROPAGATION, STABILITY