Volume 66, Issue 1-2

An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schrödinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented.

This paper investigates the synchronization problem between two unidirectionally-coupled Rössler hyperchaotic systems in the presence of noise perturbations. Sufficient conditions are obtained for synchronization by using a particularly simple linear sliding mode surface that is based on the sliding mode control concept. Only one controller function is needed to achieve synchronization in our present approach which makes it much easier to implement in contrast to many other synchronization schemes that require two or more controllers. Numerical simulation results are also included to illustrate the superior features of this new scheme.

Arising in the context of random matrix theory, the coupled Kadomtsev-Petviashvili (KP) systems have been a subject of active studies. In this paper, a coupled KP system with three potentials is investigated with symbolic computation, and the Darboux transformations of its reduced equations are obtained. Moreover, the multi-soliton-like solutions of the coupled KP system are derived. Those solutions could be of some value for the studies in the context of random matrix theory.

The separation transformation method is extended to the (1+N)-dimensional triple Sine-Gordon equation and a special type of implicitly exact solution for this equation is obtained. The exact solution contains an arbitrary function which may lead to abundant localized structures of the high dimensional nonlinear wave equations. The separation transformation method in this paper can also be applied to other kinds of high-dimensional nonlinear wave equations

The effects of wall contraction or expansion on the characteristics of the peristaltic flow have been considered in this paper. For that, we present a theoretical model of laminar incompressible viscous peristaltic flow in a deformable channel. The problem is modeled in terms of unsteady twodimensional Navier Stokes equations and the solution is obtained using the perturbation method. The physical parameters appearing due to deformation and the peristaltic motion are the wall expansion ratio (α) and the wave number (δ ), respectively. Analytic perturbation results are obtained for small wave number and small wall expansion ratio. Basically the study is undertaken to examine the peristaltic motion along with the deformation of the channel. This will enhance our understanding of deformation/squeezing and peristalsis phenomena independently and jointly. Deformation effects are shown on the otherwise peristaltic fluid flow. The results of peristaltic flow [Shapiro et al., J. Fluid Mech. Digit. Archive 37, 799 (1969)] can be recovered for the limiting case of α equal to zero.

A modified (Gʹ/G)-expansion method is proposed to construct exact solutions of nonlinear evolution equations. To illustrate the validity and advantages of the method, the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation is considered and more general travelling wave solutions are obtained. Some of the obtained solutions, namely hyperbolic function solutions, trigonometric function solutions, and rational solutions contain an explicit linear function of the variables in the considered equation. It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

Taylor-Couette flow in an annulus due to a time-dependent torque suddenly applied to one of the cylinders is studied by means of finite Hankel transforms. The exact solutions, presented under series form in terms of usual Bessel functions, satisfy both the governing equations and all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for Maxwell, second grade, and Newtonian fluids performing the same motion. Finally, some characteristics of the motion, as well as the influence of the material parameters on the behaviour of the fluid, are emphasized by graphical illustrations.

We make use of the classical correspondence between Kekulé structures and lattice paths to obtain explicit formulas for the Pauling bond order of edges in benzenoid parallelograms. These formulas are further used to establish the average π-electron content of hexagonal rings in such benzenoids. We then compare this quantity with the atom-based π-electron content of rings, and study the local and the asymptotic behaviour of their difference.

We investigate the flow of a micropolar fluid between radial stretching sheets. The magnetohydrodynamic (MHD) nonlinear problem is treated using the homotopy analysis method (HAM) and the velocity profiles are predicted for the pertinent parameters. The values of skin friction and couple shear stress coefficients are obtained for various values of Reynolds number, Hartman number, and micropolar fluid parameter.

The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randi´c connectivity indices, and the first Zagreb index. We determine the unique tree with the maximum ABC index among trees with given numbers of vertices and pendant vertices, and the n-vertex trees with the maximum, and the second, the third, and the fourth maximum ABC indices for n ≥ 6.

We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.

By means of the classical symmetry method, we investigate the two-layer model in atmosphere. The symmetry group of two-layer model equations is studied and its corresponding group invariant solutions are constructed. Ignoring the discussion of the infinite-dimensional subalgebra, we construct the optimal system of one-dimensional and two-dimensional group invariant solutions. Furthermore, using the associated vector fields of the obtained symmetry, we give out the reductions by one-dimensional and two-dimensional subalgebras, and some explicit solutions of two-layer model equations are obtained. For some interesting solutions, the figures are given out to show their properties. Some solutions can describe the horizontal structure of tropical cyclones (TC). Especially, a new solution of double-eyewall structure of TCs is firstly found in this two-layer model.

In this study, we used the homotopy perturbation method (HPM) for solving fractional nonlinear differential equations. Three models with fractional-time derivative of order α, 0<α <1, are considered and solved. The numerical results demonstrate that this method is relatively accurate and easily implemented.

Adomian decomposition and He’s variational iteration methods are analytical techniques, which can be used for solving various kinds of problems. The main property of these methods is in their flexibility and ability to solve nonlinear equations accurately. In this paper, the decomposition method and the variational iteration technique are explained, and their merits as well as their drawbacks are discussed. Then a new implementation of these methods is proposed, which yields an approximate solution with high accuracy in large regions and less computational efforts. A system of integro differential equations arising in modelling of the biological species [1] living together is employed to show how these techniques work efficiently.

This investigation looks at the peristaltic flow of a magnetohydrodynamic (MHD) Jeffrey fluid in a channel with compliant walls. The flow induced is due to sinusoidal waves on the channel walls. A series solution of the resulting boundary value problem is derived when the wave amplitude is small. Effects of various interesting flow parameters are discussed with the help of graphs

In this paper, the optimal homotopy analysis method is applied to find the solitary wave solutions of the Kuramoto-Sivashinsky equation. With three auxiliary convergence-control parameters, whose possible optimal values can be obtained by minimizing the averaged residual error, the method used here provides us with a simple way to adjust and control the convergence region of the solution. Compared with the usual homotopy analysis method, the optimal method can be used to get much faster convergent series solutions.

This paper presents results on observations of a temperature difference between the top and bottom of a vessel filled with gas in a gravitational field. The observed temperature at the top of the vessel was always lower than the temperature at the bottom of the vessel, and this temperature difference was persistent and steady over more than 20 h. The magnitude of the temperature difference depends on the types of gas molecules present but is independent of the gas pressure in the vessel within the range from 2.7×10 4 Pa to 27 Pa. A temperature difference between the top and the bottom is only observed along the vertical direction and is only observed when the vessel contains a gas. These experimental results indicate a gravity effect on molecular heat transfer which enables the transport of energy in the gas without a thermal gradient.

Biomorphic SiC/Si composites were produced from pine and beech wood, and the corresponding electrical conductivity was determined as a function of the temperature. Firstly, wood preforms were pyrolized at 1050 °C in nitrogen. Then, the pyrolized preforms were impregnated with liquid silicon and kept at 1600 °C for 2 h in vacuum. The SiC/Si composites were obtained due to the produced carbothermal reaction. As expected, the resulting electrical conductivity of these composites increased with the temperature and with the silicon content.