Natural waves in bounded and unbounded continuous media. Solitons

Abstract

As is known, the dependence of wave phase velocity on frequency is said to be dispersion. If there is dispersion then the phase velocity, i.e., the velocity of propagation of a monochromatic wave, is distinct from the so called group velocity, i.e., the velocity of propagation of a wave packet. The distinction can be both in the values of these velocities and in their directions. A dispersion law such that the directions of the phase and group velocities are the same will be called a normal dispersion law. In the case that the phase velocity is opposite in direction to the group velocity, the corresponding dispersion law we shall call anomalous.