A quasi separable dissipative Maxwell-Bloch system for laser dynamics

TL;DR

This paper introduces a novel approach to analyzing laser dynamics using a quasi separable dissipative Maxwell-Bloch system, revealing new integrals and insights into asymptotic behavior under specific parameter conditions.

Contribution

It presents a new method for separating variables in Maxwell-Bloch equations with dissipative terms, providing physical insights and conjectures on long-term laser behavior.

Findings

Existence of two time-dependent first integrals under specific conditions

A nonstandard separation of variables in the Maxwell-Bloch equations

Conjectures on asymptotic behavior of laser variables

Abstract

The Maxwell-Bloch dissipative equations describe laser dynamics. Under a simple condition on the parameters there exist two time dependent first integrals, that allow a nonstandard separation of variables in the equations. That condition has a precise physical meaning. The separated differential equations lead naturally to simple conjectures on the asymptotic behavior of the physical variables.