Instabilities of dispersion-managed solitons in the normal dispersion regime

Dispersion-managed solitons are reviewed within a Gaussian variational appr oximation and an integral evolution model. In the normal regime of the disp ersion map (when the averaged path dispersion is negative), there are two s olitons of different pulse duration and energy at a fixed propagation const ant. We show that the short soliton with a larger energy is linearly (expon entially) unstable. The other Gong) soliton with a smaller energy is linear ly stable but hits a resonance with excitations of the dispersion map. The results are compared with the results from recent publications [Bernston et al., Opt. Lett. 23, 900 (1998); Nijhof et at, ibid. 23, 1674 (1998); Grigo ryan and Menyuk, ibid. 23, 609 (1998)].