相关论文: New four-dimensional solutions of the Jacobi equat…
We derive a simple Poisson structure in the space of Fourier modes for the vorticity formulation of the Euler equations on a three-dimensional periodic domain. This allows us to analyse the structure of the Euler equations using a…
In this paper, we introduce the notion of Jacobi Novikov-Poisson algebras and demonstrate that their affinization yields Jacobi algebras. We note that every unital differential Novikov-Poisson algebra is also a Jacobi Novikov-Poisson…
A new parameterisation of the solutions of Toda field theory is introduced. In this parameterisation, the solutions of the field equations are real, well-defined functions on space-time, which is taken to be two-dimensional Minkowski space…
We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a…
In the framework of the Poisson geometry of twistor space we consider a family of perturbed 3-dimensional Kepler systems. We show that Hamilton equations of this systems are integrated by quadratures. Their solutions for some subcases are…
The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories - recently introduced by the authors - which share and generalise relevant…
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…
Jacobi sigma models are two-dimensional topological non-linear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and…
This paper introduces general methodologies for constructing closed-form solutions to linear constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in two and three spatial dimensions. Polynomial…
In this paper, we consider the hamiltonian formulation of nonholonomic systems with symmetries and study several aspects of the geometry of their reduced almost Poisson brackets, including the integrability of their characteristic…
We give a notion of compatibility between a Riemannian metric and a Jacobi structure. We prove that in case of Poisson structures, contact structures and locally conformally symplectic structures, fundamental examples of Jacobi structures,…
It is demonstrated that the knowledge of a single and arbitrary solution of the three-dimension\-al Jacobi equations allows determining infinite families of new solutions, which are generally and explicitly constructed in what follows.…
An algebra isomorphism between algebras of matrices and difference operators is used to investigate the discrete integrable hierarchy. We find local and non-local families of R-matrix solutions to the modified Yang-Baxter equation. The…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
It is known that any Poisson manifold can be embedded into a bigger space which admites a description in terms of the canonical Poisson structure, i.e., Darboux coordinates. Such a procedure is known as a symplectic realization and has a…
In this paper, we provide new exact solutions of nonlinear Klein-Gordon ($\phi^4$) equation in $1+1$-dimension. For simplicity, we focus on the static equation and ignore the time-dependence. The symmetric $\phi^4$ equation has played an…
The unimodularity condition for a Poisson structure (ie., a Poisson structure with a trivial modular class) induces a Poincar\'e duality between its Poisson homology and its Poisson cohomology. Therefore an information about the Poisson…
We provide a closed Poisson algebra involving the Ragnisco--Bruschi generalization of peakon dynamics in the Camassa--Holm shallow-water equation. This algebra is generated by three independent matrices. From this presentation, we propose a…
Fluid reductions of the Vlasov-Amp{\`e}re equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all…
We connect two a priori unrelated topics, theory of geodesically equivalent metrics in differential geometry, and theory of compatible infinite dimensional Poisson brackets of hydrodynamic type in mathematical physics. Namely, we prove that…