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A hybrid variational method of describing pulse splitting by dispersion management

Variational methods have become a widely used tool in the search for solitary waves in nonlinear systems. If a system exhibits fast oscillations in one of the degrees of freedom, its wavefunction can split into two or more separate parts and ‘orthodox’ variational descriptions are inadequate to include such nontrivial dynamics. A candidate for somewhat more realistic description is the hybrid variational method introduced by Edwards et al (2005 J. Phys. B: At. Mol. Opt. Phys. 38 363), which to our knowledge has not yet been used for a dynamical situation. Here we investigate an application of the hybrid method to a two-dimensional system with dispersion management, where pulse splitting is known to occur. By comparison with full numerical simulations, we conclude that in some cases these methods can give an improvement in the proper description of the evolution, but we also find an example where the hybrid methods fail. Edwards' method is thus evaluated in practical terms. It is hoped that this will encourage its wider use.