TY - JOUR
T1 - Separation of variables for Bi-Hamiltonian systems
JF - Math. Phys. Anal. Geom. 6 (2003) 139-179
Y1 - 2003
A1 - Gregorio Falqui
A1 - Marco Pedroni
AB - We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1598
U1 - 2520
U2 - Mathematics
U3 - Mathematical Physics
ER -