Soliton solutions of integrable systems and hirota's bilinear method
Other Title(s)
الحلول الموجبة للأنظمة التكاملية باستخدام طريقة هيروتا
Dissertant
Thesis advisor
Awawidah, Fadi Abd Allah
Jaradat, Husayn
Comitee Members
al-Shar, Safwan
al-Quran, Marwan
University
Al albayt University
Faculty
Faculty of Sciences
Department
Department of Mathematics
University Country
Jordan
Degree
Master
Degree Date
2013
English Abstract
In this thesis we investigate a general class of solutions to various partial differential equations known as solitons or stable solitary wave solutions.
We discuss and analyze the four stages of the Hirota bilinear method, for construction of soliton solutions to partial differential equations: the proper substitution to express the equation in the bilinear variables, reduction of the excess degrees of freedom, the perturbation scheme, and solution of the system of equations at the successive orders of magnitude.
The version of the equation is greatly simpli.ed by introducing a bilinear differentiation operator known as Hirota.s D-operator.
Another substitution allows Hirota.s D-operator to express the equation in a bilinear form.
This final form illustrates how the perturbation method can be used to produce exact soliton and multi-soliton solutions. We next study the simpli.ed Hirota.s bilinear method developed by Hereman.
Applications of the methods to determine multiple-soliton solutions for KdV-type, shallow water waves and Boussinesq-type equations will be given.
Main Subjects
Topics
No. of Pages
76
Table of Contents
Table of contents.
Abstract.
Introduction.
Chapter One : Soliton theory and Hirota.s bilinear method.
Chapter Two : Applications of the Hirota direct method.
Chapter Three : The simplied Hirota.s method.
Chapter Four : Soliton solutions for shallow water waves equations.
Chapter Five : The boussinesq equation.
Chapter Six : Conclusion.
References.
American Psychological Association (APA)
Muhammad, Tiber Muhammad Ali. (2013). Soliton solutions of integrable systems and hirota's bilinear method. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-420968
Modern Language Association (MLA)
Muhammad, Tiber Muhammad Ali. Soliton solutions of integrable systems and hirota's bilinear method. (Master's theses Theses and Dissertations Master). Al albayt University. (2013).
https://search.emarefa.net/detail/BIM-420968
American Medical Association (AMA)
Muhammad, Tiber Muhammad Ali. (2013). Soliton solutions of integrable systems and hirota's bilinear method. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-420968
Language
English
Data Type
Arab Theses
Record ID
BIM-420968
