In this paper, the vector parabolic equation method (VPEM) is used to investigate the Shannon capacity of multiple-input multiple-output (MIMO) communication systems in indoor corridors. This deterministic three-dimensional (3-D) full-wave method is capable to demonstrate the effects of antennas and propagation environment on the channel capacity. The VPEM can model any field depolarization eff...

We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate ~BEC! trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect ...

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the nullcontrollability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equatio...

In the present paper we find necessary and sufficient conditions on the coefficients of a parabolic equation for convexity to be preserved. A parabolic equation is said to preserve convexity if given a convex initial condition, any solution of moderate growth remains a convex function of the spatial variables for each fixed time.

We study the asymptotic behavior of stochastic hyperbolic–parabolic equations with slow–fast time scales. Both strong and weak convergence in averaging principle are established. Then we fluctuations original system around its averaged equation. show that normalized difference converges weakly to solution a linear wave An extra diffusion term appears limit which is given explicitly terms Poisso...

We define a (mean curvature flow) entropy for Radon measures in $\mathbb{R}^n$ or compact manifold. Moreover, we prove monotonicity formula of the associated with parabolic Allen-Cahn equations. If ambient manifold is non-negative sectional and parallel Ricci curvature, this consequence new equation. As an application, show that when initial data small enough (less than twice energy one-dimensi...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 1 March 2021Accepted: 27 August 2021Published online: 10 February 2022Keywordsspectral element method, Gauss--Lobatto quadrature, superconvergence, wave equation, parabolic equations, linear Schrödinger equationAMS Subject Headings65M60, 65M15, 65M06Publication DataISSN (...

In this paper homotopy perturbation method (HPM) is employed to solve two kinds of differential equations: one dimensional non homogeneous parabolic partial differential equation and non linear differential equation. Using the HPM, an exact analytical solution to non homogeneous parabolic partial differential equation and an approximate explicit solution for a non linear differential equation w...