D.Sc. (Mathematics) / In this thesis aspects of continuous symmetries of differential equations are studied. In particular the following aspects are studied in detail: Lie algebras, the Lie derivative, the jet bundle formalism for differential equations, Lie point and Lie-Backlund symmetry vector fields, recursion operators, conservation laws, Lax pairs, the Painlcve test, Lie algebra valued differenmtial forms and Dose operators as a representation of differential operators. The purpose of the study is to gain a better understanding of complicated nonlinear dirrerential equations that describe nature and to construct solutions. The differential equations under consideration were derived [rom physics and engineering. They are the following: the Kortcweg-dc Vries equation, Burgers' cquation , the sine-Gordon equation, nonlinear diffusion equations, the Klein Gordon equation, the Schrodinger equation, nonlinear Dirac equations, Yang-Mills equations, the Lorentz model, the Lotka-Volterra model, damped unharrnonic oscillators, and others. The newly found results and insights are discussed in chapters 8 to 17. Details on the COli tents of each chapter and rcfernces to some of my articles arc given in chapter 1.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:3754 |
| Date | 11 February 2014 |
| Creators | Euler, Norbert |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Johannesburg |
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