Wave packets in strongly dispersive media

An analytical study of the evolution of slowly varying wave pulses in strongly dispersive media which takes into account dispersive correction terms involving higher derivatives of the group velocity is given. A higher order differential equation for the envelope function is derived and solved recursively and by means of a procedure based on an analogy with the Schrödinger equation. The equation for the envelope function is used to obtain generalizations of the velocity of the pulse defined as the velocity of the center of inertia, and expressions are derived which determine the spreading of the pulse. Finally, we discuss how the presence of other wave modes affects the primary mode in the multimode case.