Bidifferential calculus, matrix SIT and sine-Gordon equations
Aristophanes Dimakis, Nils Kanning, Folkert Mueller-Hoissen
TL;DR
This paper develops a bidifferential calculus framework for matrix SIT equations, providing a method to generate exact solutions and deriving a solution formula for the sine-Gordon equation.
Contribution
It introduces a novel bidifferential calculus approach to matrix SIT equations and offers a general solution-generating technique, including a sine-Gordon solution formula.
Findings
Derived an infinite family of exact solutions for matrix SIT equations.
Established a solution formula for the sine-Gordon equation.
Demonstrated the applicability of bidifferential calculus to integrable systems.
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.
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