Relativistic effects in non-relativistic systems

We propose a new model for describing the evolution of scalar optical pulses in Kerr-type planar waveguides and optical fibres. The wave envelope satisfies a dimensionless equation and its solutions are thus endowed with some intriguing and mystical properties. By considering the behaviour of the governing equation under various sets of coordinate transformations, we have found that our new model can be interpreted within the framework of Einstein’s special theory of relativity. This leads to a range of new physical predictions that have no counterpart in conventional pulse theory. Exact analytical bright and dark solitons have been derived by applying various mathematical techniques, and the space-time geometry of these new self-localized stationary light structures has been explored in detail. Further analysis and simulations have confirmed the robustness of Helmholtz pulse solitons in the face of perturbations to their temporal shape, which is nice