Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability , transformations and relativity

The origin of conventional models for nonlinear optical pulse propagation lies in the ubiquitous slowly-varying envelope approximation (SVEA) accompanied by a Galilean boost to a local-time frame. While such a near-universal procedure typically results in a simpler (parabolic) model of the nonlinear Schrödinger-type, in reality a more subtle but less well-explored class of wave equation underpins the propagation problem. In reassessing the way conventional models treat the linear part of the wave operator (by omitting the “SVEA + Galilean boost” device), we have uncovered a powerful and elegant framework for describing time-domain nonlinear optical phenomena that has strong overlaps with Einstein’s special theory of relativity. Here, we generalize our scalar modelling to accommodate two coupled waves experiencing spatiotemporal dispersion and cubic nonlinearity. A range of analytical methods has been deployed to derive new families of phasetopological vector solitons (dark-bright and darkdark), and their stability properties investigated using new numerical algorithms.