Article ID Journal Published Year Pages File Type
9877679 Physica D: Nonlinear Phenomena 2005 18 Pages PDF
Abstract
The focusing nonlinear Schrödinger equation at critical dimension is considered in the presence of a weak damping, either linear or involving a power of the wave intensity. Special attention is paid to the case of a diffusive damping term, that describes Landau damping for a low-frequency Alfvén wave subject to filamentation instability. When compared with the nonlinear damping classically used to model multi-photon absorption in nonlinear optics, significant differences concerning the wave energy dissipation are numerically observed and interpreted by means of an asymptotic ODE model resulting from a modulation analysis of the solution near collapse. It is in particular shown that whereas for a nonlinear damping, dissipation is almost totally concentrated in the collapse events, it remains sizeable while the wave defocuses when the damping is linear.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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