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

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.

References in corpus (5)

• Stability of equilibria for the $\mathfrak{so}(4)$ free rigid body
• Stability problem for the torque-free gyrostat by using algebraic methods
• Stability of equilibrium states in the Zhukovski case of heavy gyrostat using algebraic methods
• Invariant critical sets of conserved quantities
• A note on stability of the vertical uniform rotations of the heavy top

Cited by in corpus (4)

• Symmetries of the Maxwell-Bloch equations with the rotating wave approximation
• A note on stability of spacecrafts and underwater vehicles
• Applications of nonlocal constants of motion in Lagrangian Dynamics
• Stability analysis and control chaos for fractional 5D Maxwell-Bloch model