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Hamiltonian Hierarchies on Semisimple Lie Algebras
Author(s) -
Sattinger D. H.
Publication year - 1985
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198572165
Subject(s) - mathematics , integrable system , meromorphic function , lie algebra , hamiltonian (control theory) , pure mathematics , algebra over a field , partial differential equation , connection (principal bundle) , nonlinear system , mathematical analysis , physics , quantum mechanics , mathematical optimization , geometry
A recursion formula is described which generates infinite hierarchies of completely integrable Hamiltonian systems of nonlinear partial differential equations. These equations govern the evolution of a function u of x , t which takes its values in a semisimple Lie algebra. A Hamiltonian for the hierarchy is given in terms of a meromorphic connection matrix.