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Some Hamiltonian operators in infinite dimensional Hamiltonian systems. (Chinese) Zbl 0725.58020
Summary: Some Hamiltonian operators with special forms are presented. Firstly, the sum operators of a class of u-linear differential operators of the first order and constant coefficient differential operators are discussed, and the necessary and sufficient conditions for them to be Hamiltonian are obtained. Based on these conditions, one typical case is analyzed. Next, three Hamiltonian operators are generated directly from infinite dimensional Lie algebras. Thirdly, a kind of matrix differential operators corresponding to the structural functions of the second degree is constructed and an algebraic description for them to be Hamiltonian is proposed.
MSC:
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
70H05Hamilton’s equations
35Q72Other PDE from mechanics (MSC2000)