Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics

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