The stability problem and special solutions for the 5-components Maxwell-Bloch equations

TL;DR

This paper thoroughly analyzes the stability of equilibria in the 5-components Maxwell-Bloch system, constructs homoclinic orbits, and identifies a variety of explicit periodic solutions, advancing understanding of its dynamical behavior.

Contribution

It provides a complete stability analysis, explicit construction of homoclinic orbits, and uncovers a rich family of periodic solutions for the 5-components Maxwell-Bloch equations.

Findings

Complete stability characterization of isolated equilibria.

Explicit construction of homoclinic orbits using symplectic geometry.

Discovery of a rich family of explicit periodic solutions.

Abstract

For the 5-components Maxwell-Bloch system the stability problem for the isolated equilibria is completely solved. Using the geometry of the symplectic leaves, a detailed construction of the homoclinic orbits is given. Studying the problem of invariant sets for the system we discover a rich family of periodic solutions in explicit form.