On solving nonlinear partial differential equations in mathematical physics

Other Title(s)

بعض خواص حلول المعادلات التفاضلية
Some properties of solutions of differential equations

Dissertant

Abd al-Aziz, Mahmud Ahmad Muhammad

Thesis advisor

Zayid, al-Sayyid Muhammad al-Sayyid

University

Omdurman Islamic University

Faculty

Faculty of Sciences and Technology

Department

Department of Mathematics

University Country

Sudan

Degree

Master

Degree Date

2011

English Abstract

With the aid of symbolic computation, the exact solutions of nonlinear partial differential equations have been investigated in this thesis.

Some powerful methods have been presented such as : the generalized (G1 / G)−expansion method, the generalized extended (G1 / G)−expansion method, the extended tanh-function method,the generalized tanh-coth function method and the exp-function method.

In the first chapter, the introduction is introduced.

In the second chapter, the generalized (G1 / G)−expansion method is presented to derive the traveling wave solutionsfor some nonlinear PDEs via the nonlinear KdV equation with variable coefficients, the Burgers equation with variable coefficients, the combined KdV-Burgers equation with variable coefficients, the Burgers-Fisher equation with variable coefficients, the variable coefficients Burgers-Fisher equation with the forced term, the generalized Gardner equation with variable coefficients, the variable coefficients generalized Gardner equation with the forced term and the generalized Zakharov-Kuznetsov equation with variable coefficients.

In the third chapter, we use the generalized extended(G1 / G)−expansion method to derive the traveling wave solutions for the generalized nonlinear variable coefficients Schrödinger equation with the gain and the higher-order nonlinear Schrödinger equation with variable coefficients. In section 4.2 of the fourth chapter, we use the extended tanh-function method to derive the traveling wave solutions for some nonlinear PDEs via the combined KdV-Burgers equation with variable coefficients, the KdV equation with variable coefficients and forcing term, the generalized Gardner equation with variable coefficients and the generalized nonlinear variable coefficients Schrödinger equation. In section 4.3 of the fourth chapter, we use the generalized tanh-coth function method to construct the traveling wave solutions for two nonlinear PDEs via the modified KdV equation with variable coefficients and the Sawada-Kotera equation with variable coefficients.

In the fifth chapter, the exp-function method is presented to derive the traveling wave solutions for some nonlinear PDEs via the nonlinear dispersive equation with variable coefficients, the generalized Camassa-Holm equation with variable coefficients, the generalized K(n,n) equation with variable coefficients, the generalized BBM equation with variable coefficients, the generalized nonlinear variable coefficients Schrödinger equation (GNLS) and the combined KdV-Burgers equation with variable coefficients.

These methods are important because the more and different types solutions which are obtained can be applied to a wide range of problems in science and engineering.

Main Subjects

Mathematics

Topics

• Mathematical physics

No. of Pages

222

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-362593