Bidifferential Calculus, Matrix SIT and Sine-Gordon Equations

Abstract

We express a matrix version of the self-induced transparency (SIT) equations in the bidifferential calculus framework. An infinite family of exact solutions is then obtained by application of a general result that generates exact solutions from solutions of a linear system of arbitrary matrix size. A side result is a solution formula for the sine-Gordon equation.

Keywords

• bidifferential calculus
• integrable system
• self-induced transparency
• sine-Gordon