Unstable behavior of dispersion-managed (DM) solitons in a system with lumped filtering is numerically studied. A variational analysis shows that the system cannot have stable fixed DM soliton solutions when the filter location is improperly chosen. This is because of the unique dynamics of the spectral behavior of DM solitons, which differs from that of standard solitons in fibers with constant dispersion. The instability is confirmed by numerical simulations with and without sliding center frequencies of the filters.
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