Sine-Gordon Equation

Abstract

The equation φtt − φxx + m2 sin φ = 0 is presented as a model field theory and studied in detail. It exhibits discrete conserved quantities and extended particle states, with the proper behavior regarding covariance, stability, etc. Those particles do not interact with small oscillations, and we show that this (plus a few reasonable requirements) defines the model uniquely. A connection with the Korteweg-de Vries equation, which has similar properties, is established.