Integrable quadratic Hamiltonians on so(4) and so(3,1)

Abstract

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.

16 pages

References in corpus (6)

• Integrable systems on $so(4)$ related with XXX spin chains with boundaries
• Factorization of the current algebra and integrable top-like systems
• On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops
• Classification of integrable quadratic Hamiltonians on e(3)
• On a 'Mysterious' Case of a Quadratic Hamiltonian
• Applications of CRACK in the Classification of Integrable Systems

Cited by in corpus (4)

• On bi-hamiltonian structure of some integrable systems on so*(4)
• Integrable Systems Related to Deformed $\mathfrak{so}(5)$
• On a 'Mysterious' Case of a Quadratic Hamiltonian
• Factorization problem with intersection