Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2003-09-09
Nonlinear Sciences
Pattern Formation and Solitons
13 pages, 9 figures; to appear in SIAM Journal of Applied Mathematics
Scientific paper
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.
Barashenkov Igor V.
Zemlyanaya E. V.
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