‎in this paper‎, ‎we investigate a damped korteweg-de‎ ‎vries equation with forcing on a periodic domain‎ ‎$mathbb{t}=mathbb{r}/(2pimathbb{z})$‎. ‎we can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic.

An integral equation approach is developed for the problem of determining the steady-state current to a periodic array of microelectrodes imbedded in an otherwise insulating plane. The formulation accounts for both surface electrode and bulk fluid reactions, and evaluates the Green’s functions for periodic systems using convergence acceleration techniques. Numerical results are presented for di...

The best method for investigating moiré phenomena in the superposition of periodic layers is based on the Fourier approach. However, superposition moiré effects are not limited to periodic layers, and they also occur between repetitive structures that are obtained by geometric transformations of periodic layers. We present in this paper the basic rules based on the Fourier approach that govern ...

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

This paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities, using Homotopy Perturbation Method with an auxiliary term (HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass, and quintic nonlinear beam are investigated to exhibit the reliability and ability of the p...

The paper proposes an efficient method to analyze the response of periodic structures to non-periodic excitations in the time domain, employing the Finite-Difference Time-Domain (FDTD) method. To that end, the array-scanning method, which has been previously associated with frequency-domain, integral formulations of periodic structure problems, is translated into the context of FDTD. Hence, the...

We give a uniied approach to error estimates for periodic interpolation on full and sparse grids in certain Sobolev spaces. We imposèperiodic' Strang{Fix conditions on the underlying functions in order to obtain error bounds with explicit constants. x1. Introduction The approximation and interpolation of bivariate periodic functions have been studied for some time. While periodic interpolation ...

We implement the new transform method for solving boundary value problems developed by Fokas for periodic boundary conditions. The approach presented here is not a replacement for classical methods nor is it necessarily an improvement. However, in addition to establishing that periodic problems can indeed be solve by the new transform method (which enhances further its scope and applicability),...

Periodic orbits of nonlinear mappings are very useful for the study of dynamical systems. In this paper, a new approach for computing periodic orbits through the global minimization of a properly defined objective function, using the Particle Swarm Optimization method, is introduced. Experimental results on wellknown and widely used nonlinear mappings indicate that the algorithm is robust, it i...