QCD motivated effective models coupled with the cosmological dilaton field are analyzed. It is shown that all models possess confining solutions with the linear potential of confinement even thought such solutions are not observed in the original effective theory. In case of the Pagels-Tomboulis model analytical solutions are explicit found.

In nonlinear self-consistent system, Lorenz system (Lorenz equations) is a classic case with chaos solutions which are sensitively dependent on the initial conditions. As it is difficult to get the analytical solution, the numerical methods and qualitative analytical methods are widely used in many studies. In these papers, Runge-Kutta method is the one most often used to solve these differenti...

The focus of this paper is on traveling wave solutions of the equation u t + f(u) x = u xx + 2 u xxx ; in which the ux function f is trilinear and nonconvex. In particular, it is shown that for combinations of parameters in certain ranges, there are traveling waves that converge as ?! 0 to undercompressive shocks, in which the characteristics pass through the shock. The analysis is based on exp...

Group theoretical methods are used to study the equations describing x :x (2) cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions...

In this paper, the approximate analytical solutions of a general diffusion equation with fractional time derivative in the presence of a linear external force are obtained with the help of the homotopy perturbation method (HPM). The explicit solutions of the problem for the initial condition as a function of x have been obtained. It reveals that a few iterations are needed to obtain accurate ap...

This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differ...

An original approach is presented to the timedependent thermal modelling of complex 3-dimensional electronic systems, from metallised power FETs and MMICs, though MCMs, up to circuit board level. This method o ers a powerful alternative to conventional numerical thermal simulation techniques. In contrast to semi-analytical Fourier approaches involving DFT-FFT, the method is based on explicit, f...

This paper presents explicit analytical solutions of the pressure coefficient and the pressure ratio across the oblique shock and expansion waves in function of the flow deflection angle. These new explicit pressure-deflection solutions can be efficiently used in solving applied aerodynamic problems in supersonic flows, such as the aerodynamics of airfoils and wings in supersonic-hypersonic flo...

Radon-222 diffusion in an anhydrous andesitic melt was investigated. The melts were glass discs formed artificially from melted volcanic materials. Solutions of the relevant diffusion equations were done by the explicit finite difference method. Results were compared to analytical solutions reported in the literature and good agreement was found. We have shown that the explicit finite differenc...

Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...