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A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent...

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent...

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent...

In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative \(f^{\prime }(x)\) by Hermite interpolation operator \(H_{2n+1}(f;x)\) based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil...

The current work highlights the following issues: a brief survey of the development in the theory of fractional differential equations has been raised. A very recent technique based on the generalized Taylor series called—residual power series (RPS)—is introduced in detailed manner. The time-fractional foam drainage equation is considered as a target model to test the validity of...

The nonlinear partial differential equation of Harry Dym is generalized by replacing the first-order time derivative by a fractional derivative of order \(\alpha ,\; 0 \le \alpha \le 2\). The aim of the present paper is to obtain an approximate solution of time fractional generalized Harry Dym equation using Adomian Decomposition Method (ADM). The fractional derivative is...

University of Science and Technology, Irbid 22110, Jordan
Received 4 January 2013; Accepted 1 March 2013
Academic Editor: Anjan Biswas
Copyright © 2013 **Marwan** **Alquran** et al. This is an open access article

Purpose This paper proposes the use of different analytical methods in obtaining approximate solutions for nonlinear differential equations with oscillations. Methods Three methods are considered in this paper: Lindstedt-Poincare method, the Krylov-Bogoliubov first approximate method, and the differential transform method. Results Figures that are given in this paper give a...

PurposeThis paper investigates an analytical solution to a physical model called (2 + 1)-dimensional Zoomeron equation.MethodsThe solutions of Zoomeron are obtained using direct methods such as the extended tanh, the exponential function and the sech p −tanh p function methods.ResultsSeveral soliton solutions are obtained using the proposed methods.ConclusionsThe obtained...

We study two-component evolutionary systems of a homogeneous KdV equations of second and third order. The homotopy analysis method (HAM) is used for analytical treatment of these systems. The auxiliary parameter h of HAM is freely chosen from the stability region of the h-curve obtained for each proposed system.