Abstract: This manuscript focuses attention on new exact solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The extended trial equation method (ETEM), which is one of the analytical methods, has been handled for finding exact solutions of the system of equations for the ion sound wave and...

block-flexure is the most common mode of toppling failure in natural and excavated rock slopes. in such failure, some rock blocks break due to tensile stresses and some overturn under their own weights and then all of them topple together. in this paper, first, a brief review of previous studies on toppling failures is presented. then, the physical and mechanical properties of experimental mode...

the analytical theory of one dimensional, dispersion free miscible displacement of oil by injection gas with nc component has shown that: the mmp is the lowest pressure at which any one of the initial oil, injection gas or crossover key tie lines becomes critical, which means that its length approaches to zero. in this paper, we propose a method for a solving multi component system based on ana...

Analytical solutions to the time-dependent Schrödinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single rea...

We present a simulation algorithm that accurately propagates a molecule pair using large time steps without the need to invoke the full exact analytical solutions of the Smoluchowski diffusion equation. Because the proposed method only uses uniform and Gaussian random numbers, it allows for position updates that are two to three orders of magnitude faster than those of a corresponding scheme ba...

In this paper, Homotopy Analysis Method (HAM) is applied to obtain approximate analytical solution of modified Kuramoto–Sivashinsky (KS) equation. HAM provides a simple way to adjust and control the convergence region of the series solution by introducing several parameters, namely, the auxiliary parameter, h, the auxiliary function, H(x, t), the initial guess, u0(x, t) and the auxiliary linear...

We consider periodic solution for coupled systems of mass-spring. Three practical cases of these systems are explained and introduced. An analytical technique called Parameter Expansion Method PEM was applied to calculate approximations to the achieved nonlinear differential oscillation equations. Comparing with exact solutions, the first approximation to the frequency of oscillation produces t...