On the local systems hamiltonian in the weakly nonlocal Poisson brackets. Abstract We consider nonlocal field-theoretical Poisson brackets containing the operator of integration in the nonlocal part. The main attention is given to the nonlocal brackets of Hydrodynamic Type for which we introduce the Physical and Canonical forms. We use the Canonical form of these brackets for the investigation ...

We derive nonlocal coupled-mode equations for a Bragg grating embedded in a medium with nonlocal nonlinearity. Using these equations, we study the oscillatory instability of nonlocal Bragg solitary waves and demonstrate that collisions between them result in fusion into a standing pulse or breather , possibly with generation of additional jets, in a broad range of parameters. The results are ex...

A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given.

The interrelations between weight-function upscaling (measurement) and the definition of various nonlocal operators is explored. Let < f > = f∗g where f∗g is the convolution product which represents the effect of upscaling via an instrument (defined by g) on a field variable f and its localized counterpart. Nonlocal field variables are defined and employed for upscaling. In this talk it will be...

We consider the basic SIR epidemiological model with the Michaelis-Menten formulation of the contact rate. From the study of Michaelis-Menten basic enzymatic reaction, we design two types of Nonstandard Finite Difference (NSFD) schemes for the SIR model: Exact-related schemes based on the Lambert W function and schemes obtained by using Mickens’s rules of more complex denominator functions for ...

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is la...

We consider dislocations in the framework of Eringen’s nonlocal elasticity. The fundamental field equations of nonlocal elasticity are presented. Using these equations, the nonlocal force stresses of a straight screw and a straight edge dislocation are given. By the help of these nonlocal stresses, we are able to calculate the interaction forces between dislocations (Peach-Koehler forces). All ...

This paper is concerned with the existence of mild solutions to a class of semilinear differential inclusions with nonlocal conditions. By using the fixed point theory for multivalued maps, we get some general results on nonlocal differential inclusions, which include some recent results on nonlocal problems as special cases. An example of partial differential equations is provided to illustrat...

On the local systems hamiltonian in the weakly nonlocal Poisson brackets. Abstract We consider nonlocal field-theoretical Poisson brackets containing the operator of integration in the nonlocal part. The main attention is given to the nonlocal brackets of Hydrodynamic Type for which we introduce the Physical and Canonical forms. We use the Canonical form of these brackets for the investigation ...

High frequency integrable regimes in nonlocal nonlinear optics. Abstract We consider an integrable model which describes light beams propagating in nonlocal nonlinear media of Cole-Cole type. The model is derived as high frequency limit of both Maxwell equations and the nonlocal nonlinear Schrödinger equation. We demonstrate that for a general form of nonlinearity there exist selfguided light b...