Traveling wave solutions of 3+1-dimensional Boiti–Leon–Manna–Pempinelli equation by using improved tanh([Formula presented])-expansion method

Aim of this article is to investigate soliton solutions of recently developed 3+1-dimensional Boiti–Leon–Manna–Pempinelli equation by utilizing newly derived approach namely, improved tanh([Formula presented])-expansion method. As a result, we succeed to secure various types of new solutions for this model including kink, periodic rational solutions. Some of the derived solutions has been discussed in the form of 2-,3-dimensional graphs and their contour plots to visualize the wave dynamics graphically. The results generated by this technique proves that it is a straightforward, robust, and effective method to generate variety of solutions and can be applied on different nonlinear models

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

1 p. -- [Editorial Material

Approximate analysis of population dynamics with density-dependent migrations and the Allee effects

Purpose - The aim of this paper is to present the numerical simulation of the population dynamics model with density-dependent migrations and the Allee effects using the homotopy perturbation method (HPM). Design/methodology/ approach - The paper applied HPM and the results obtained by this method are compared to the exact solution. The results show applicability, accuracy and efficiency of HPM in solving the transient non-linear advection-diffusion- reaction equation. Findings - In this study, HPM is applied to solve the model of population dynamics with density- dependent migrations and the Allee effects. Numerical approximations show a high degree of accuracy. The numerical results we obtained justify the advantage of this methodology, even in the few terms approximation is accurate. Errors can be made smaller by taking new terms of the iteration formulas. Originality/value - It is confirmed that the work has not been published in any other journal. © 2012 Emerald Group Publishing Limited

Analytical solutions to the pulsed Klein-Gordon equation using Modified Variational Iteration Method (MVIM) and Boubaker Polynomials Expansion Scheme (BPES)

WOS: 000277746000004In this study, we propose an analytical solution to the Klein-Gordon equation in a pulsed stationary regime. The performed protocols are based on the modified variational iteration method MVIM and Boubaker polynomials expansion scheme BPES. The results are presented, and compared with some solutions proposed later in order to confirm the good accuracy of the protocols used. (C) 2009 Elsevier Ltd. All rights reserved