Related papers: On Hamiltonian Structures of Partial Difference Eq…

Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…

The Miura transformation plays a crucial role in the study of integrable systems. There have been various extensions of the Miura transformation, which have been used to relate different kinds of integrable equations and to classify the…

We investigate the bi-Hamiltonian structures associated with constrained dispersionless modified KP hierarchies which are constructed from truncations of the Lax operator of the dispersionless modified KP hierarchy. After transforming their…

For a linear non-Hermitian system, I demonstrate that a Hamiltonian can be constructed such that the non-Hermitian equations can be expressed exactly in the form of Hamilton's canonical equations. This is first shown for discrete systems…

As a continuation of Rabei et al. work [11], the Hamilton- Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton- Jacobi function in configuration space is obtained…

We explore variational Poisson-Nijenhuis structures on nonlinear PDEs and establish relations between Schouten and Nijenhuis brackets on the initial equation with the Lie bracket of symmetries on its natural extensions (coverings). This…

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…

Based on ideas due to Scovel-Weinstein, I present a general framework for constructing fluid moment closures of the Vlasov-Poisson system that exactly preserve that system's Hamiltonian structure. Notably, the technique applies in any space…

Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…

A four-field reduced model of single helicity, incompressible MHD is derived in cylindrical geometry. An appropriate set of noncanonical variables is found, and the Hamiltonian, the Lie-Poisson bracket and the Casimir invariants are…

We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We…

In order to describe the impact of different geometric structures and constraints for the dynamics of a Hamiltonian system, in this paper, for a magnetic Hamiltonian system defined by a magnetic symplectic form, we first drive precisely the…

We construct local bihamiltonian structures from classical $W$-algebras associated to non-regular nilpotent elements of regular semisimple type in Lie algebras of type $A_2$ and $A_3$. They form exact Poisson pencil, admit a dispersionless…

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…

Let $M$ be a smooth closed orientable manifold and $\mathcal{P}(M)$ the space of Poisson structures on $M$. We construct a Poisson bracket on $\mathcal{P}(M)$ depending on a choice of volume form. The Hamiltonian flow of the bracket acts on…

We introduce a natural class of multicomponent local Poisson structures $\mathcal P_k + \mathcal P_1$, where $\mathcal P_1$ is a local Poisson bracket of order one and $\mathcal P_k$ is a homogeneous Poisson bracket of odd order $k$ under…

The Hamiltonian formulation of Mimetic Gravity is formulated. Although there are two more equations than those of general relativity, these are proved to be the constraint equation and the conservation of energy-momentum tensor. The Poisson…

One of the remarkable properties of cluster algebras is that any cluster, obtained from a sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the initial cluster (known as the "Laurent phenomenon").…

First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson…

In this paper, generalizing the construction of \cite{HP1}, we equip the relative moduli stack of complexes over a Calabi-Yau fibration (possibly with singular fibers) with a shifted Poisson structure. Applying this construction to the…