Instabilities of dispersion-managed solitons in the normal dispersion regime

Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of different pulse duration and energy at a fixed propagation constant. We show that the short soliton with a larger energy is linearly (exponentially) unstable. The other (long) soliton with a smaller energy is linearly 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 al., ibid. 23, 1674 (1998); Grigoryan and Menyuk, ibid. 23, 609 (1998)].