Related papers: Mechanical Equations on Bi-Para Conformal Geometry

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…

This is a revised version of the paper submitted before.

The SL(2,R) invariant Hamiltonian systems are discussed within the frame- work of the orbit method. It is shown that both dynamics and symmetry trans- formations are globally well-defined on phase space. The flexibility in the choice of…

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…

Some fixed point results are given for a class of functional contractions over partial metric spaces. These extend some contributions in the area due to Ilic et al [Math. Comput. Modelling, 55 (2012), 801-809].

A way to add an extra dimension is briefly discussed.

The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.

In this study, we introduce Euler-Lagrange and Hamiltonian equations on (R2; g; J) being a model of para-Kaehlerian Space Forms. Finally, some geometrical and physical results on the related mechanic systems have been discussed.

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…

This work is devoted to study the deformation of spacetime metrics as generalized conformal transformations. Some applications are also considered, in particular the equations of motion in deformed spacetime are studied.

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

The connection between differential geometry of curves and the (2+1)-dimensional integrable spin system - the M-III equation is established. Using the presented geometrical formalism the L-equivalent counterpart of the M-III equation is…

An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.

When in general geometric backgrounds the metric is accompanied by torsion, the metric conformal properties should correspondingly be followed by analogous torsional conformal properties; however a combined metric torsional conformal…

We apply geometric tools to study dynamics of two- and threepeakon solutions of the Camassa--Holm equation. New proofs of asymptotic behavior of the solutions are given. In particular we recover well-known collision conditions. Additionally…

A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…

The purpose of this paper is to define some notions of movability for morphisms of inverse systems which extend the movability properties of inverse systems and which are compatible with the equivalence relations which define pro-morphisms…

We show that the equations underlying the $GW$ approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact,…

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.