Abdul-Majid Wazwaz

Partial Differential Equations and Solitary Waves Theory

Partial Differential Equations.- Basic Concepts.- First-order Partial Differential Equations.- One Dimensional Heat Flow.- Higher Dimensional Heat Flow.- One Dimensional Wave Equation.- Higher Dimensional Wave Equation.- Laplaces Equation.- Nonlinear Partial Differential Equations.- Linear and Nonlinear Physical Models.- Numerical Applications and Pade Approximants.- Solitons and Compactons.- Solitray Waves Theory.- Solitary Waves Theory.- The Family of the KdV Equations.- KdV and mKdV Equations of Higher-orders.- Family of KdV-type Equations.- Boussinesq, Klein-Gordon and Liouville Equations.- Burgers, Fisher and Related Equations.- Families of Camassa-Holm and Schrodinger Equations.

A reliable modification of Adomian decomposition method

In this paper we propose a powerful modification of Adomian decomposition method that will accelerate the rapid convergence of the series solution. The validity of the modified technique is verified through illustrative examples. In all cases of differential and integral equations, we obtained excellent performance from the modified algorithm. The modification could lead to a promising approach for many applications in applied sciences.

A new algorithm for calculating adomian polynomials for nonlinear operators

In this paper, a reliable technique for calculating Adomian polynomials for nonlinear operators will be developed. The new algorithm offers a promising approach for calculating Adomian polynomials for all forms of nonlinearity. The algorithm will be illustrated by studying suitable forms of nonlinearity. A nonlinear evolution model will be investigated.

A sine-cosine method for handlingnonlinear wave equations

In this paper, we establish exact solutions for nonlinear wave equations. A sine-cosine method is used for obtaining traveling wave solutions for these models with minimal algebra. The method is applied to selected physical models to illustrate the usage of our main results.

A first course in integral equations

Classifications of Integral Equations Fredholm Integral Equations Volterra Integral Equations Fredholm Integro-Differential Equations Volterra Integro-Differential Equations Singular Integral Equations Nonlinear Fredholm Integral Equations Nonlinear Volterra Integral Equations Applications of Integral Equations

The tanh method for traveling wave solutions of nonlinear equations

In this work we employ the tanh method for traveling wave solutions of nonlinear equations. The study is extended to equations that do not have tanh polynomial solutions. The efficiency of the method is demonstrated by applying it for a variety of selected equations.

A new algorithm for solving differential equations of Lane-Emden type

In this paper, a reliable algorithm is employed to investigate the differential equations of Lane-Emden type. The algorithm rests mainly on the Adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point. The proposed framework is applied to a generalization of Lane-Emden equations so that it can be used in differential equations of the same type.

A new method for solving singular initial value problems in the second-order ordinary differential equations

Singular initial value problems, linear and nonlinear, homogeneous and nonhomogeneous, are investigated by using Adomian decomposition method. The solutions are constructed in the form of a convergent series. A new general formula is established. The approach is illustrated with few examples.

A new modification of the Adomian decomposition method for linear and nonlinear operators

In this paper we present an efficient modification of the Adomian decomposition method that will facilitate the calculations. We then conduct a comparative study between the new modification and the modified decomposition method. The study is conducted through illustrative examples. The new modification introduces a promising tool for many linear and nonlinear models.

New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations

The genuinely nonlinear dispersive K(m,n) equation, ut+(um)x+(un)xxx=0, which exhibits compactons: solitons with compact support, is investigated. New solitary-wave solutions with compact support are developed. The specific cases, K(2,2) and K(3,3), are used to illustrate the pertinent features of the proposed scheme. An entirely new general formula for the solution of the K(m,n) equation is established, and the existing general formula is modified as well.