• Login
  • Help Guide
View Item 
  •   JOOUST IR Home
  • Theses & Dissertations
  • Doctor of Philosophy Theses and Dissertations
  • School of Biological, Physical, Mathematics & Actuarial Sciences
  • View Item
  •   JOOUST IR Home
  • Theses & Dissertations
  • Doctor of Philosophy Theses and Dissertations
  • School of Biological, Physical, Mathematics & Actuarial Sciences
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Lie Symmetry Analysis of Nonlinear Fourth Order Evolution Equation

Thumbnail
Publication Date
2020
Author
Wambura, Kevin Odundo
Type
Thesis
Metadata
Show full item record
Abstract/Overview

Problems involving nonlinear partial differential equations arise in various fields of science for instance in propagation of shallow water waves, fluid physics. quantum mechanics. chemical kinematics and other related areas. Therefore, the task of obtaining the exact solutions to a nonlinear partial differential equation is of great importance and has attracted high attention among researchers. Nikolai and Maria made an attempt. in obtaining the exact solution of a special nonlinear fourth order evolution equation expressed as using Newton polygon method. The method allowed them to express the exact. solution of the equation studied through the solution of another equation using the properties of the basic equation itself. However, they were only able to obtain one exact. solution of the equation. In the recent years, lie symmetry analysis has played a significant. role in the construction of exact solutions to nonlinear evolution equations. The history of Lie symmetry group classification method goes back to Sophus Lie at the end of the 19th century. A variety of methods have been developed in the past few years by Ovsyarrnikov. Ibragimov and others. Therefore, by setting the coefficient of the nonlinear term uu; to zero, we have attempted in this study to determine more than one exact explicit solution of the nonlinear fourth order evolution equation using Lie symmetry analysis approach. The equation is a Korteweg-De Vries (KdV) type of equation this {at has been applied to describe a wide range of physical phenomena of the evolution and interaction to nonlinear waves. such as fluid dynamics, aerodynamics, continuum mechanics, solitons and turbulence. The exact solutions to the nonlinear fourth order evolution equation has been obtained through the prolongation of infinitesimal generators, determination of geometric vector fields, similarity reduction and use of power series method. We believe this will be a great contribution to the knowledge and further research.

Publisher
JOOUST
Permalink
http://ir.jooust.ac.ke:8080/xmlui/handle/123456789/10908
Collections
  • School of Biological, Physical, Mathematics & Actuarial Sciences [55]

Browse

All of JOOUST IRCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

LoginRegister

Statistics

View Usage Statistics

Contact Us

Copyright © 2023-4 Jaramogi Oginga Odinga University of Science and Technology (JOOUST)
P.O. Box 210 - 40601
Bondo – Kenya

Useful Links

  • Report a problem with the content
  • Accessibility Policy
  • Deaccession/Takedown Policy

TwitterFacebookYouTubeInstagram

  • University Policies
  • Access to Information
  • JOOUST Quality Statement