The fractional cable equation is studied on a bounded space domain. One of the prescribed boundary conditions is of Dirichlet type, the other is of a general form, which includes the case of nonlocal boundary conditions. In real problems nonlocal boundary conditions are prescribed when the data on the boundary can not be measured directly. We apply spectral projection operators to convert the p...

We give the Lax representations for for the elliptic, hyperbolic and homogeneous second order Monge-Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Mong...

For the nonlocal T-periodic Gross–Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter , → 0, up to O(3/2) have been constructed. The quasi-energy spectral series found correspond to the closed phase trajectories of the Hamilton–Ehrenfest system which are stable in the linear approximation. The monodromy operator of this equation has been constructed to with...

We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the nonlocal Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all the...

Intervals of the parameter λ are determined for which there exist positive solutions for the system of nonlinear differential equations, u(n) + λa(t)f(v) = 0, v(n)+λb(t)g(u) = 0, for 0 < t < 1, and satisfying three-point nonlocal boundary conditions, u(0) = 0, u(0) = 0, . . . , u(n−2)(0) = 0, u(1) = αu(η), v(0) = 0, v(0) = 0, . . . , v(n−2)(0) = 0, v(1) = αv(η). A Guo-Krasnosel’skii fixed point...

We study the effect of photoinhibition in a nonlocal reaction-diffusionadvection equation, which models the dynamics of a single phytoplankton species in a water column where the growth of the species depends solely on light. Our results show that, in contrast to the case of no photoinhibition, where at most one positive steady state can exist, the model with photoinhibition possesses at least ...

Range-separated (screened) hybrid functionals provide a powerful strategy for incorporating nonlocal exact (Hartree-Fock-type) exchange into density functional theory. Existing implementations of range separation use a fixed system-independent screening parameter. Here, we propose a novel method that uses a position-dependent screening function. These locally range-separated hybrids add substan...