Since the heady days of pioneering temporal optical soliton research [1–3], pulse propagation equations have been almost exclusively of the nonlinear Schrödinger form. These parabolic models are derived from Maxwell''s equations through a careful handling of the linear dispersion operator, and invoking the near-universal slowly-varying envelope approximation (SVEA). A more general approach to pulse evolution, and hence a potentially more accurate one, may clearly be adopted by seeing what progress can be made when the SVEA is relaxed. When one does so, the governing equation is of the Helmholtz (elliptic or hyperbolic) type. While the precedent of using these more sophisticated models was set in the late 1970s [4], they appear to have received relatively little subsequent attention in the literature. A notable exception is the recent paper by Biancalana and Creatore [5], giving Helmholtz-type pulse models a new physical context in the guise of spatial dispersion.
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