In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied. Mathematics subject classification (2010). 35K57 ·...

The absorbing "ricepile" model with stochastic toppling rules has been numerically studied. Local limited, local unlimited, nonlocal limited, and nonlocal unlimited versions of the absorbing model have been investigated. Transport properties and different dynamical regimes of all of the models have been analyzed, from the point of view of self-organized criticality. Phase transitions between di...

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of smal...

This paper presents an image interpolation model with nonlocal p-Laplacian regularization. The nonlocal p-Laplacian regularization overcomes the drawback of the partial differential equation PDE proposed by Belahmidi and Guichard 2004 that image density diffuses in the directions pointed by local gradient. The grey values of images diffuse along image feature direction not gradient direction un...

The purpose of this paper is to compare the solutions of one-dimensional boundary value problems corresponding to classical, fractional and nonlocal diffusion on bounded domains. The latter two diffusions are viable alternatives for anomalous diffusion, when Fick’s first law is an inaccurate model. In the case of nonlocal diffusion, a generalization of Fick’s first law in terms of a nonlocal fl...

Direct algebraic method of obtaining exact solutions to nonlinear PDE’s is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions.

This is a synopsis and extension of Phys. Rev. D49 5408 (1994). The Pseudodual Chiral Model illustrates 2-dimensional field theories which possess an infinite number of conservation laws but also allow particle production, at variance with naive expectations—a folk theorem of integrable models. We monitor the symmetries of the pseudodual model, both local and nonlocal, as transmutations of the ...

Quantum mechanics permits nonlocality—both nonlocal correlations and nonlocal equations of motion—while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality— “superquantum” correlations, and nonlocal “jamming” of correlations—and derive new results for the jammi...

We analyze a finite volume scheme for nonlocal SIR model, which is a nonlocal reaction-diffusion system modeling an epidemic disease. We establish existence solutions to the finite volume scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general L compactness criterion.

where D is a certain function of the electric field. For derivation of such type of equation see [1, 2]. Recent theoretical and experimental results highlight a very interesting phenomenology, such as “accessible solitons”, collapse arrest, optical vortices (see e.g. [3−6] and references therein), associated with so-called nonlocal nonlinear media. Most of the models studied before are not inte...