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Exact Solutions of Evolution Equations with Variable Coefficients - Couverture souple

Osman, Mohamed Safaa; Abdel-Gawad, H. I.

 
9783659634468: Exact Solutions of Evolution Equations with Variable Coefficients
Couverture souple
ISBN 10 : 3659634468 ISBN 13 : 9783659634468
Editeur : LAP LAMBERT Academic Publishing, 2014

Synopsis

In this book, we make an extension to the unified method that unifies all the known methods in the literature for finding the exact solutions of scalar or vector nonlinear PDE's with constant coefficients in the nonlinear sciences. The extended unified method unable us to investigate the effects of the inhomogeneity of the diffusion, diffraction dispersion super-diffusion of the medium trough considering the coefficients space-dependent. On the other hand, some problems have been studied when these coefficients are taken as time-dependent. The main objectives of the extended unified method are; (a) Constructing the necessary conditions for the existence of solutions to evolution equations. (b) Whenever the solutions exist, this method suggests a new classification to the solution structures namely; the polynomial solutions, the rational solutions and the polynomial-rational solutions. In each type, we mean that the obtained equations are accomplished by a set of auxiliary equation whose solution gives rise to an auxiliary function.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

In this book, we make an extension to the unified method that unifies all the known methods in the literature for finding the exact solutions of scalar or vector nonlinear PDE's with constant coefficients in the nonlinear sciences. The extended unified method unable us to investigate the effects of the inhomogeneity of the diffusion, diffraction dispersion super-diffusion of the medium trough considering the coefficients space-dependent. On the other hand, some problems have been studied when these coefficients are taken as time-dependent. The main objectives of the extended unified method are; (a) Constructing the necessary conditions for the existence of solutions to evolution equations. (b) Whenever the solutions exist, this method suggests a new classification to the solution structures namely; the polynomial solutions, the rational solutions and the polynomial-rational solutions. In each type, we mean that the obtained equations are accomplished by a set of auxiliary equation whose solution gives rise to an auxiliary function.

Biographie de l'auteur

Dr. Mohamed Safaa Mohamed Osman. A lecturer of Applied Mathematics at Cairo University, Giza, Egypt. He obtained his PhD from Cairo University, Giza, Egypt in 2014. His research interests include: Fractional Calculus. Mathematical Modeling in Biology, Medicine, Chemistry and Physics. Stability analysis of Dynamical systems.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2014
Langue
anglais
ISBN 10 
3659634468
ISBN 13 
9783659634468
Reliure
Broché
Nombre de pages
116
Coordonnées du fabricant
non disponible
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