Lie-Poisson bifurcations for the Maxwell-Bloch equations

Conference · Mon Jan 01 04:00:00 EST 1990

OSTI ID:6682524

David, D

We present a study of the set of Maxwell-Bloch equations on R{sup 3} from the point of view of Hamiltonian dynamics. These equations are shown to be bi-Hamiltonian, on the one hand, and to possess several inequivalent Lie-Poisson structures, on the other hand, parametrized by the group SL(2,R). Each structure is characterized by a particular distinguished function. The level sets of this function provide two-dimensional surfaces onto which the motion takes various symplectic forms. 4 refs.

• Research Organization: Los Alamos National Lab., NM (USA)
• Sponsoring Organization: DOE/MA
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6682524
• Report Number(s): LA-UR-90-2271; CONF-9005237--2; ON: DE90015035
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BLOCH EQUATIONS
COMMUTATORS
DIFFERENTIAL EQUATIONS
EQUATIONS
HAMILTONIANS
LIE GROUPS
MATHEMATICAL OPERATORS
MAXWELL EQUATIONS
NONLINEAR OPTICS
NONLINEAR PROBLEMS
OPTICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SYMMETRY GROUPS
TRAVELLING WAVES