135 research outputs found
Traveling solitons in the damped driven nonlinear Schr\"odinger equation
The well known effect of the linear damping on the moving nonlinear
Schr\"odinger soliton (even when there is a supply of energy via the spatially
homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero
momentum does not necessarily mean zero velocity. We show that two or more
parametrically driven damped solitons can form a complex traveling with zero
momentum at a nonzero constant speed.
All traveling complexes we have found so far, turned out to be unstable.
Thus, the parametric driving is capable of sustaining the uniform motion of
damped solitons, but some additional agent is required to stabilize it.Comment: 13 pages, 9 figures; to appear in SIAM Journal of Applied Mathematic
Parametrically Driven Dark Solitons
We show that unlike the bright solitons, the parametrically driven kinks are
immune from instabilities for all dampings and forcing amplitudes; they can
also form stable bound states. In the undamped case, the two types of stable
kinks and their complexes can travel with nonzero velocities.Comment: 4 pages; 2 figures; to appear in PR
Soliton complexity in the damped-driven nonlinear Schr\"odinger equation: stationary, periodic, quasiperiodic complexes
Stationary and oscillatory bound states, or complexes, of the damped-driven
solitons are numerically path-followed in the parameter space. We compile a
chart of the two-soliton attractors, complementing the one-soliton attractor
chart.Comment: 12 pages, 7 figure
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