Bargmann Type Systems for the Generalization of Toda Lattices | Zendy

Fang Li | Zendy; Liping Lu | Zendy

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Bargmann Type Systems for the Generalization of Toda Lattices

Author(s) -

Fang Li,

Liping Lu

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/287529

Subject(s) - integrable system , toda lattice , mathematics , symplectic geometry , pure mathematics , eigenfunction , hamiltonian system , generalization , hierarchy , lattice (music) , symplectomorphism , hamiltonian (control theory) , mathematical analysis , mathematical physics , eigenvalues and eigenvectors , physics , quantum mechanics , mathematical optimization , economics , acoustics , market economy

Under a constraint between the potentials and eigenfunctions, the nonlinearization of the Lax pairs associated with the discrete hierarchy of a generalization of the Toda lattice equation is proposed, which leads to a new symplectic map and a class of finite-dimensional Hamiltonian systems. The generating function of the integrals of motion is presented, by which the symplectic map and these finite-dimensional Hamiltonian systems are further proved to be completely integrable in the Liouville sense. Finally, the representation of solutions for a lattice equation in the discrete hierarchy is obtained

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