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العنوان
Exact Solutions and Geometrical Properties of some Nonlinear PDEs in Mathematical Physics Using Different Expansion Methods /
المؤلف
Abu-amra, Safaa Soliman Mohammad Rizk.
هيئة الاعداد
باحث / صفاء سليمان محمد رزق ابوعمره
مشرف / عبدالرحمن محمد شحاته
مشرف / فتحي ابراهيم عبدالبصير
الموضوع
Mathematical physics. Differential equations, Nonlinear.
تاريخ النشر
2019.
عدد الصفحات
157 p. :
اللغة
الإنجليزية
الدرجة
الدكتوراه
التخصص
الرياضيات (المتنوعة)
تاريخ الإجازة
1/1/2019
مكان الإجازة
جامعة المنيا - كلية العلوم - رياضيات بحتة
الفهرس
Only 14 pages are availabe for public view

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Abstract

The Nonlinear partial differential equations are widely used models for a great number of problems in the fields of physics, chemistry and biology, and have gained a surge of attention from mathematicians ever since they were derived. In addition, the solution of these equations is very important and the studies on it have never stopped.
There are many methods for obtaining the exact solutions of nonlinear partial differential equations such as the inverse scattering method, Hirota’s bilinear method, Backlund transformation ,homogeneous balance method, tanh-function method, Jacobi elliptic function expansion method, (G′/G)-expansion function method and modified (w/g)-expansion method.
In this thesis, we got new exact solutions to some of the nonlinear partial differential equations, using the modified (w/g)- expansion method and its different forms. Also A variation of (G’⁄G)-expansion method with the study of its Geometrical Properties.
The thesis contains six chapters: In the first chapter we studied the definition of nonlinear partial differential equations, basic concepts and some references used in this thesis. In the second chapter we got the new traveling wave solutions for some nonlinear partial differential equations by using modified (w/g)- expansion method. In the third chapter we obtained accurate solutions to some equations by the variation (G ′/G) method. In the chapter four we studied the geometric properties and exact solutions of some nonlinear evolutionary equations in mathematical physics using different expansion methods. In chapter five we also studied a comparison of the exact solutions of the Boussinesq equation by applying different expansion methods. In chapter six we gave discussions and conclusions of this work