Generalized Expansion Method Research Articles

Three-dimensional cylindrical Kadomtsev–Petviashvili equation in a dusty electronegative plasma

AbstractThe hydrodynamic equations of positive and negative ions, Boltzmann electron density distribution and Poisson equation with stationary dust particles are used along with the reductive perturbation method to derive a three-dimensional cylindrical Kadomtsev–Petviashvili equation. The generalized expansion method, used to obtain a new class of solutions, admits a train of well-separated bell-shaped periodic pulses. At certain condition, these periodic pulses degenerate to solitary wave solutions. The effects of the physical parameters on the solitary pulses are examined. Finally, the present results should elucidate the properties of ion-acoustic solitary pulses in multi-component plasmas, particularly in Earth's ionosphere.

Performance optimization of open zero-buffer multi-server queueing networks

Open zero-buffer multi-server general queueing networks occur throughout a number of physical systems in the semi-process and process industries. In this paper, we evaluate the performance of these systems in terms of throughput using the generalized expansion method (GEM) and compare our results with simulation. Secondly, we embed the performance evaluation in a multi-objective optimization setting. This multi-objective optimization approach results in the Pareto efficient curves showing the trade-off between the total number of servers used and the throughput. Experiments for a large number of settings and different network topologies are presented in detail.

A generalized expansion method for nonlinear wave equations

A generalized Jacobian/exponential expansion method for finding the exact traveling wave solutions of a nonlinear partial differential equation is discussed. We use this method to construct many new, previously undiscovered exact solutions for the Boussinesq and modified KdV equations. We also apply it to the shallow long wave approximate equations. New solutions are deduced for this system of partial differential equations.

Nonlinear structures: Explosive, soliton, and shock in a quantum electron-positron-ion magnetoplasma

Theoretical and numerical studies are performed for the nonlinear structures (explosive, solitons, and shock) in quantum electron-positron-ion magnetoplasmas. For this purpose, the reductive perturbation method is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining extended quantum Zakharov–Kuznetsov equation. The latter has been solved using the generalized expansion method to obtain a set of analytical solutions, which reflects the possibility of the propagation of various nonlinear structures. The relevance of the present investigation to the white dwarfs is highlighted.

New exact solutions for a generalized variable-coefficient KdV equation

New exact solutions for a generalized variable-coefficient KdV equation were obtained using the generalized expansion method [R. Sabry, M.A. Zahran, E.G. Fan, Phys. Lett. A 326 (2004) 93]. The obtained solutions include solitary wave solutions besides Jacobi and Weierstrass doubly periodic wave solutions.

Nonlinear quantum dust acoustic waves in nonuniform complex quantum dusty plasma

The quantum hydrodynamic model for plasmas is employed to study the dynamics of the nonlinear quantum dust acoustic (QDA) wave in a nonuniform quantum dusty plasma (QDP). Through the reductive perturbation technique, it is shown that the quantum hydrodynamical basic equations describing the nonlinear QDA waves yield a modified Korteweg-de Veries equation with slowly varying coefficients in the system inhomogeneity. Applying generalized expansion method, it is found that the system admits only rarefactive solitons. The properties of the solitons such as the velocity, the amplitude and the width of the nonlinear QDA waves are analyzed using appropriate choice for initial ion and electron density numbers. For the homogeneous QDP, no critical value is found. Because of the system inhomogeneity, a new criticality is found forcing with the usage of new stretching coordinates. A higher evolution equation with third-order nonlinearity is derived at the critical values. The solution of the latter equation admits rarefactive shock wave attached with an amplitude factor. The present investigations should be useful for researches on astrophysical plasmas as well as for ultra small micro- and nano-electronic devices.

Nonlinear dust acoustic waves in a nonuniform magnetized complex plasma with nonthermal ions and dust charge variation

Propagations of nonlinear dust acoustic (DA) solitary waves and shock waves in a nonuniform magnetized dusty plasma are investigated. The incorporation of the combined effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium values of particle density, charging variable, and particle potential on the waves leads to a significant modification to the nature of nonlinear DA solitary waves. The nonlinear wave evolution is governed by a modified Zakhavov-Kusnetsov-Burgers (MZKB) equation, whose coefficients are space dependent. Using a generalized expansion method, new solutions for the MZKB equation are obtained. The form of solutions consists of two parts; one of them is the amplitude factor and the other is a superposition of bell-shaped and kink-type shock waves. New solutions are classified into three categories. A type of the solution is determined depending on the nonthermal parameter. Findings in this investigation should be useful for understanding the ion acceleration mechanisms close to the Moon and also enhancing our knowledge on pickup ions around unmagnetized bodies, such as comets, Mars, and Venus, including medium inhomogeneities with nonadiabatic dust charging processes.

A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found.

Symbolic Computation and Construction of Soliton-Like Solutions to the (2+1)-Dimensional Breaking Soliton Equation**The project supported by National Natural Science Foundation of China under Grant No. 1007201 and the National Key Basic Research Development Project Program under Grant No. G1998030600

Based on the computerized symbolic system Maple, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new general ansätz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, , and obtain rich new families of the exact solutions of the breaking soliton equation, including the non-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular function solutions.

Multi-objective routing within large scale facilities using open finite queueing networks

The major objective of this paper is to examine the optimal routing in layout and location problems from a network optimization perspective where manufacturing facilities are modelled as open finite queueing networks with a multi-objective set of performance measures. The overall material handling system is broken down into a set of layout topologies. For each one of these topologies the optimal routing is determined so that the product throughput is maximized while minimizing the average sojourn time and holding costs. An approximate analytical decomposition technique for modelling open finite queueing networks, called the Generalized Expansion Method (GEM), developed by the authors, is utilized to calculate the desired outputs. A mathematical optimization procedure which is described in this paper is then used to determine the optimal routes. As will be demonstrated, the design methodology of combining the optimization and analytical queueing network models provides a very effective procedure for evaluating alternative topologies while simultaneously determining the average sojourn times and the maximum throughputs of the best routes.

The generalized expansion method for open finite queueing networks

Blocking makes the exact analytical analysis of open queueing networks with finite capacities intractable except for very small networks, therefore, approximation approaches are needed to analyze these types of networks. For exponential open finite queueing networks, some methods have been proposed but little has been done so far on nonexponential open finite queueing networks. This paper introduces a new approximation technique for the analysis of general open finite queueing networks. Extensive numerical examples are performed for different network topologies and the results are compared with simulation.