A Hierarchy of Discrete Integrable Equation and its Hamiltonian Structure
نویسندگان
چکیده
In this paper a new discrete isospectral problem is constructed, from which a new Lax integrable discrete equation is generated and obtain its hierarchy structure. The Hamiltonian structures for the hierarchy of the Lax integrable discrete equation is established by using the trace identity which was proposed by Tu.
منابع مشابه
On the quantum KP hierarchy and its relation to the non-linear Schrödinger equation
We establish a relation between the classical non-linear Schrödinger equation and the KP hierarchy, and we extend this relation to the quantum case by defining a quantum KP hierarchy. We also present evidence that an integrable hierarchy of equations is obtained by quantizing the first Hamiltonian structure of the KdV equation. The connection between infinite-dimensional algebras and integrable...
متن کاملA Lax Operator Hierarchy for the New Fifth Order Integrable System
We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.
متن کاملLiouville Correspondence Between the Modified KdV Hierarchy and Its Dual Integrable Hierarchy
We study an explicit correspondence between the integrable modified KdV hierarchy and its dual integrable modified Camassa-Holm hierarchy. A Liouville transformation between the isospectral problems of the two hierarchies also relates their respective recursion operators, and serves to establish the Liouville correspondence between their flows and Hamiltonian conservation laws. In addition, a n...
متن کاملA Super-Integrable Hierarchy and Its Super-Hamiltonian Structure
It has been an important and interesting topic in soliton theory for searching for new Lax integrable or Liouville integrable systems as many as possible such that they are associated with certain evolution equations with physical meaning. The simple and efficient method to obtain continuous or discrete integrable systems was proposed Tu. Ma developed it and called it Tu scheme. By taking advan...
متن کاملThe Supersymmetric Two Boson Hierarchy
We summarize all the known properties of the supersymmetric integrable Two Boson equation. We present its nonstandard Lax formulation and tri-Hamiltonian structure, its reduction to the supersymmetric nonlinear Schrödinger equation and the local as well as nonlocal conserved charges. We also present the algebra of the conserved charges and identify its second Hamiltonian structure with the twis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008