Extending Hamiltonian operators to get bi-Hamiltonian coupled KdV systems
نویسندگان
چکیده
منابع مشابه
Extending Hamiltonian Operators to Get Bi-Hamiltonian Coupled KdV Systems
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of lower order, new local bi-Hamiltonian coupled KdV systems are proposed. As a consequence of bi-Hamiltonian structure, they all possess infinitely many symmetrie...
متن کاملA Class of Coupled KdV Systems and Their Bi-Hamiltonian Formulation
Bi-Hamiltonian formulation is significant for investigating integrable properties of nonlinear systems of differential equations [1] [2] [3]. Many mathematical and physical systems have been found to possess such kind of bi-Hamiltonian formulation. There are two important problems related to bi-Hamiltonian theory. The one is which kind of systems can possess bi-Hamiltonian formulation and the o...
متن کاملBi–Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables
We discuss from a bi-Hamiltonian point of view the Hamilton–Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi–bi– Hamiltonian formulation of Pfaffian type. This property allows us to straightforwardly recover a set of separation variables for the corresponding Hamilton–Jacobi equation.
متن کاملQuantum Bi-Hamiltonian Systems
We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.
متن کاملCompletely Integrable Bi-hamiltonian Systems
We study the geometry of completely integrable bi-Hamiltonian systems, and in particular, the existence of a bi-Hamiltonian structure for a completely integrable Hamiltonian system. We show that under some natural hypothesis, such a structure exists in a neighborhood of an invariant torus if, and only if, the graph of the Hamiltonian function is a hypersurface of translation, relative to the af...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physics Letters A
سال: 1998
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(98)00555-6