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Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

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...

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

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...

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

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...

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

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...

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

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...

Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials

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...

Analytical solutions of fractional foam drainage equation by residual power series method

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...

An approximate solution for a fractional model of generalized Harry Dym equation

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...

Analytical Study of Some Important Generalized Nonlinear Partial Differential Equations

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

Effective approximate methods for strongly nonlinear differential equations with oscillations

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...

Mathematical methods for a reliable treatment of the (2+1)-dimensional Zoomeron equation

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...

Solitonic Solutions for Homogeneous KdV Systems by Homotopy Analysis Method

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.