Showing papers in "Communications in Nonlinear Science and Numerical Simulation in 2009"

TL;DR: In this article, the basic ideas and current developments of the homotopy analysis method, an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers, are described.

TL;DR: In this paper, it is shown that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x−1/2.

TL;DR: In this paper, the homotopy analysis method is applied to solve linear and nonlinear fractional initial-value problems (fIVPs), and the fractional derivatives are described by Caputo's sense.

TL;DR: Results of the various types of analysis suggest that the proposed image encryption technique is able to manage the trade offs between the security and speed and hence suitable for the real-time secure image and video communication applications.

TL;DR: In this article, the magnetohydrodynamic (MHD) flow over a shrinking sheet is solved analytically in a closed-form equation and is an exact solution of the full governing Navier-Stokes equations for the problem.

TL;DR: In this article, the effect of the slip, the magnetic, and the mass transfer parameters on MHD flow under slip condition over a permeable stretching surface is solved analytically.

TL;DR: In this article, the synchronization conditions of fractional order chaotic systems with activation feedback method were analyzed and the synchronization of commensurate order hyperchaotic Lorenz system of the base order 0.98 was implemented based on this method.

TL;DR: In this paper, a fractional chaotic communication method using an extended fractional Kalman filter is presented, where the chaotic synchronization is implemented by the EFKF design in the presence of channel additive noise and processing noise.

TL;DR: In this article, the authors analyze the common errors of the recent papers in which the solitary wave solutions of nonlinear differential equations are presented and classify seven common errors, and illustrate several cases when authors present some functions for describing solutions but do not use arbitrary constants.

TL;DR: In this article, the authors used the homotopy analysis method to detect the fin efficiency of convective straight fins with temperature-dependent thermal conductivity, compared with those of the exact solution and Adomian's decomposition method.

TL;DR: In this article, a control law is proposed to realize finite-time chaos synchronization for the unified chaotic system with uncertain parameters, which is simple, robust and only part parameters are required to be bounded.

TL;DR: In this paper, a sliding mode control design for fractional order systems with input and state time-delay is proposed, and the existence of the sliding mode and the stability of the proposed control design are discussed.

TL;DR: In this paper, the homotopy analysis method (HAM) is implemented for finding approximate solutions of the Burger and regularized long wave (RLW) equations, and the results of the proposed method are compared with the results obtained by HPM.

TL;DR: In this paper, the authors adopt the homotopy analysis method (HAM) to obtain solutions of linear and nonlinear fractional diffusion and wave equation, where the fractional derivative is described in the Caputo sense.

TL;DR: In this article, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical system, and the synchronization and the corresponding complexity for multiple slave systems with multiple master systems are discussed.

TL;DR: In this article, an analysis is performed to find the series solution of the boundary layer Falkner-Skan equation for wedge, which takes into account a special form of the chosen magnetic field.

TL;DR: In this paper, the authors discuss the selection of the initial approximation, auxiliary linear operator, auxiliary function, and convergence control parameter in the application of the homotopy analysis method, in a fairly general setting.

TL;DR: A cipher feedback is used to change the state value of the tent map, which makes the S-boxes relate to the plaintext and enhances the confusion and diffusion properties of the cryptosystem.

TL;DR: In this article, the peristaltic transport of MHD Newtonian fluid in a symmetric, two-dimensional channel with variable viscosity under the influence of heat transfer analysis is considered.

TL;DR: In this article, the nonsingular terminal sliding mode control for chaotic systems with uncertain parameters or disturbances is considered and the switching surface is designed technically to realize fast convergence and it can stabilize the chaotic systems in a finite time.

TL;DR: In this article, the synchronization problem of coupled Chua's circuits generator of n-scroll chaotic attractors in master-slave configuration is numerically studied, and a potential application to transmit encrypted audio and image information is also given.

TL;DR: In this article, a SIS epidemic model incorporating media coverage is presented, and the dynamics of this disease model under constant and pulse vaccination are analyzed, and stability analysis of the model with constant vaccination shows that the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and if the endemic equilibrium exists.

TL;DR: In this article, the homotopy analysis method has been employed to obtain solutions of a system of nonlinear fractional partial differential equations, which indicates the validity and great potential of the Homotopy Analysis method for solving system of fractional PDEs.

TL;DR: In this article, an analytic method for strongly nonlinear problems, namely the homotopy analysis method (HAM), is applied to give convergent series solution of non-similarity boundary-layer flows.

TL;DR: In this article, an application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed, and the typical mistakes of application of this method are demonstrated.

TL;DR: Based on emergy synthesis, a comparative study on constructed wetland (CW) and conventional wastewater treatments with three representative cases in Beijing is presented in this article, which reveals that CWs are environment-benign, less energy-intensive despite the relatively low ecological waste removal efficiency (EWRE), and less cost in construction, operation and maintenance compared with the conventional wastewater treatment plants.

TL;DR: In this article, the authors used the homotopy analysis method (HAM) to evaluate the analytical approximate solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient.

TL;DR: In this article, the Korteweg-de Vries and the Burgers equations were considered using the travelling wave and the general solutions of these equations were presented using the traveling wave.

TL;DR: Alizadeh-Pahlavan et al. as mentioned in this paper investigated the effects of parameters such as elasticity number, magnetic number, radiative heat transfer, Prandtl number, and Eckert number on the temperature field above the sheet.

TL;DR: In this paper, the G ′ G -expansion method was used to construct exact travelling wave solutions of nonlinear evolution equations, the balance numbers of which are not positive integers.