Spatiotemporal Dispersion and Wave Envelopes with Relativistic and Pseudorelativistic Characteristics

A generic nonparaxial model for pulse envelopes is presented. Classic Schrödinger-type descriptions of wave propagation have their origins in slowly-varying envelopes combined with a Galilean boost to the local time frame. By abandoning these two simplifications, a picture of pulse evolution emerges in which frame-of-reference considerations and space-time transformations take center stage. A wide range of effects, analogous to those in special relativity, then follows for both linear and nonlinear systems. Explicit demonstration is presented through exact bright and dark soliton pulse solutions.