Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems

A generic envelope equation is proposed for describing the evolution of scalar pulses in systems with spatiotemporal dispersion and cubic-quintic nonlinearity. Our analysis has application, for instance, in waveguide optics where the physical origin of the dielectric response lies in the χ(3) and χ(5) susceptibilities. Exact analytical bright and gray solitons are derived by coordinate transformations and methods of direct integration. Known solitons of conventional pulse theory (based on nonlinear-Schrödinger prescriptions) are shown to emerge asymptotically as subsets of the more general spatiotemporal solutions, and simulations test the stability of the latter through a class of perturbed initial-value problem