Related papers: Variational Poisson-Nijenhuis structures for parti…
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…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
We introduce a notion of compatibility between (almost) Dirac structures and (1,1)-tensor fields extending that of Poisson-Nijenhuis structures. We study several properties of the "Dirac-Nijenhuis" structures thus obtained, including their…
We develop a rigorous theory of non-local Poisson structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard-Magri scheme of integrability to a…
Based on the non-Abelian Lie algebra, a generalized geometric Lie bracket on vector space is proposed to further realize the generalized structural Poisson bracket, and then we briefly discuss the second order equations of the generalized…
We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of…
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Liouville equation, from the view point of the general T-system and Y-system. We also study the…
We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets…
This paper aims to construct two graded Lie algebras associated with a nonsymmetric operad with multiplication. Maurer-Cartan elements of these graded Lie algebras correspond respectively to Nijenhuis elements and Rota-Baxter elements for…
Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order…
The interconnection between self-duality, conformal invariance and Lie-Poisson structure of the two dimensional non-abelian Thirring model is investigated in the framework of the hamiltonian method.
The super or Z_2-graded Schouten-Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors \Lambda of even order. The…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
We show that the space of observables of test particles carries a natural Jacobi structure which is manifestly invariant under the action of the Poincar\'{e} group. Poisson algebras may be obtained by imposing further requirements. A…
A general approach is proposed to constructing covariant Poisson brackets in the space of histories of a classical field-theoretical model. The approach is based on the concept of Lagrange anchor, which was originally developed as a tool…
This paper investigates different Poisson structures that have been proposed to give a Hamiltonian formulation to evolution equations issued from fluid mechanics. Our aim is to explore the main brackets which have been proposed and to…
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…
We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
We discuss a system of third order PDEs for strictly convex smooth functions on domains of Euclidean space. We argue that it may be understood as a closure of sorts of the first order prolongation of a family of second order PDEs. We…