Abstract. A fully discrete a priori analysis of the finite element heterogenenous multiscale method (FE-HMM) introduced in [A. Abdulle, M. Grote, C. Stohrer, Multiscale Model. Simul. 2014] for the wave equation with highly oscillatory coefficients over long time is presented. A sharp a priori convergence rate for the numerical method is derived for long time intervals. The effective model over ...

Abstract. We study the homogenization and singular perturbation of the wave equation in a periodic media for long times of the order of the inverse of the period. We consider inital data that are Bloch wave packets, i.e., that are the product of a fast oscillating Bloch wave and of a smooth envelope function. We prove that the solution is approximately equal to two waves propagating in opposite...

In the present paper, authors are interested in studying a famous nonlinear PDE referred to as $(2+1)$-dimensional chiral Schrödinger (2D-CS) equation with applications mathematical physics. this respect, real and imaginary portions of 2D-CS firstly derived through traveling wave transformation. Different structures equation, classified bright dark solitons, then retrieved using modified Kudrya...

with the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. many site-specific methods have been proposed for modeling indoor radio channels. among these methods, the ray tracing algorithm and the finite-difference time domain (fdtd) method are the most popular ones. the ray tracing approach ...

In this research work, we successfully construct various kinds of exact traveling wave solutions such as trigonometric like, singular and periodic well hyperbolic to the (2+1)-dimensional Chiral nonlinear Schröginger equation (CNLSE) which is used a governing discuss in quantum field theory. The mechanisms are obtain these extended rational sine-cosine/sinh-cosh constraint conditions for existe...

We solve the Cauchy problem for the n-dimensional wave equation, where n is an odd integer, using elementary properties of the Fourier transform. We also show that the solution can be obtained by invoking Bessel functions. The wave equation has a rich history fraught with controversy, both mathematical, see [9], and physical, see [16]. It all started in 1747 when d’Alembert, in a memoir present...

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...