135 research outputs found

    Traveling solitons in the damped driven nonlinear Schr\"odinger equation

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    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

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    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

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    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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