Envelope-soliton propagation for three interacting waves in a dispersive medium

Abstract

An initial value problem is set up to describe propagation of a low-frequency Wave-field interacting with two almost transparent wave-fields in a dispersive medium. With no linear loss, perfect phase-matching, and equal group velocities for the two high-frequency wave-packets, it is shown how the solution of the above problem can evolve to well-known soliton solutions of the sine-Gordon equation. Other attempts for solving the more general problem in which all the group velocities are different are also discussed.