Dispersion-managed solitons via an averaged variational principle

Constrained minimization is used as a computational strategy to approximate and study dispersion-managed solitons through their characterization as minima of an averaged variational principle. A basis of Hermite–Gaussian functions is used and the constrained minimization procedure is carried out to find such pulses. This method produces more accurate pulse shapes than the usual Gaussian approximations, propagating with less noise and providing a far better representation of the tail of the pulse. The success of this procedure provides confirmation that the dispersion-managed soliton is truly a minimum of the constrained variational principle. When the residual dispersion is negative, the dispersion-managed soliton can no longer be a minimum—a fact that is confirmed by our numerical simulations. Even in this case, however, approximate pulse shapes can be obtained using this finite dimensional approximation. Additionally, we find critical points other than the ground state. The most interesting is an excited bound state corresponding to a symmetric bisoliton.