相关论文: Hamiltonian Structure of PI Hierarchy
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector…
This work is devoted to the establishment of a Poisson structure for a format of equations known as Generalized Lotka-Volterra systems. These equations, which include the classical Lotka-Volterra systems as a particular case, have been…
The Painlev\'e transcendents $P_{\rom{I}}$--$P_{\rom{V}}$ and their representations as isomonodromic deformation equations are derived as nonautonomous Hamiltonian systems from the classical $R$--matrix Poisson bracket structure on the dual…
The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present…
We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless…
We introduce two families of soliton hierarchies: the twisted hierarchies associated to symmetric spaces. The Lax pairs of these two hierarchies are Laurent polynomials in the spectral variable. Our constructions gives a hierarchy of…
It is well known that isomonodromic deformations admit a Hamiltonian description. These Hamiltonians appear as coefficients of the characteristic equations of their Lax matrices, which define spectral curves for linear systems of…
It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra,…
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and…
A Poisson structure on the time-extended space R x M is shown to be appropriate for a Hamiltonian formalism in which time is no more a privileged variable and no a priori geometry is assumed on the space M of motions. Possible geometries…
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…
It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then…
In this paper, we consider the generalized isomonodromic deformations of rank two irregular connections on the Riemann sphere. We introduce Darboux coordinates on the parameter space of a family of rank two irregular connections by apparent…
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…
We calculate, in a relatively explicit way, the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces. A corollary is that the Hamiltonian…
In literature, it is known that any solution of Painlev\'{e} VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on $\mathbb{CP}^{1}$. In this paper, we extend this isomonodromy theory on…
Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential…
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is…
We study the Poisson structure associated to the defocusing Ablowitz-Ladik equation from a functional-analytical point of view, by reexpressing the Poisson bracket in terms of the associated Caratheodory function. Using this expression, we…