Related papers: The Hamiltonian structure of discrete KP equations
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…
We introduce the notion of a multiplicative Poisson $\lambda$-bracket, which plays the same role in the theory of Hamiltonian differential-difference equations as the usual Poisson $\lambda$-bracket plays in the theory of Hamiltonian PDE.…
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…
The analogue of the Poisson bracket for the De Donder-Weyl (DW) Hamiltonian formulation of field theory is proposed. We start from the Hamilton- Poincar\'{e}-Cartan (HPC) form of the multidimensional variational calculus and define the…
The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An…
In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton--Jacobi theory for continuous contact…
In this paper, a novel discrete algebra is presented which follows by combining the SU(2) Lie-Poisson bracket with the discrete Frenet equation. Physically, the construction describes a discrete piecewise linear string in R3. The starting…
The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of…
We analyze the symplectic structure on the dressing group in the \shG\, model by calculating explicitly the Poisson bracket $\{g\x g\}$ where $g$ is the \dg\, element which creates a generic one soliton solution from the vacuum. Our result…
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models ${\sl cKP}_{R,M}$, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an…
We introduce a bracket on 1-forms defined on ${\cal J}^{\infty}(S^1, \mathbb{R}^n)$, the infinite jet extension of the space of loops and prove that it satisfies the standard properties of a Poisson bracket. Using this bracket, we show that…
We introduce an efficient split finite element (FE) discretization of a y-independent (slice) model of the rotating shallow water equations. The study of this slice model provides insight towards developing schemes for the full 2D case.…
The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one…
The time evolution in a supersymmetric extension of the Kodomtsev-Petviashvilli hierarchy, a classical integrable system, is shown to be Hamiltonian. The canonical bracket associated to the Hamiltonian evolution is the classical analog of…
We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies…
The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity…
We propose one possible generalization of the KP hierarchy, which possesses multi bi--hamiltonian structures, and can be viewed as several KP hierarchies coupled together.
The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general bi-Hamiltonian…
It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally in an extension of the formal variational calculus incorporating divergences. The linear spaces of local…
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…