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1 
Lie symmetry analysis of certain nonlinear evolution equations of mathematical physics / Abdullahi Rashid Adem.Adem, Abdullahi Rashid January 2013 (has links)
In this work we study the applications of Lie symmetry analysis to certain nonlinear
evolution equations of mathematical physics. Exact solutions and conservation laws
are obtained for such equations. The equations which are considered in this thesis
are a generalized Kortewegde VriesBurgers equation, a twodimensional integrable
generalization of the KaupKupershmidt equation, a coupled Kortewegde Vries system,
a generalized coupled variablecoefficient modified Kortewegde Vries system, a
new coupled Kortewegde Vries system and a new coupled KadomtsevPetviashvili
system.
The generalized Kortewegde VriesBurgers equation is investigated from the point
of view of Lie group classification. We show that this equation admits a fourdimensional
equivalence Lie algebra. It is also shown that the principal Lie algebra
consists of a single translation symmetry. Several possible extensions of the principal
Lie algebra are computed and their associated symmetry reductions and exact
solutions are obtained.
The Lie symmetry method is performed on a twodimensional integrable generalization
of the KaupKupershmidt equation. Exact solutions are obtained using the
Lie symmetry method in conjunction with the extended tanh method and the extended
Jacobi elliptic function method. In addition to exact solutions we also present
conservation laws which are derived using the multiplier approach.
A coupled Kortewegde Vries system and a generalized coupled variablecoefficient
modified Kortewegde Vries system are investigated using Lie symmetry analysis.
The similarity reductions and exact solutions with the aid of simplest equations
and Jacobi elliptic function methods are obtained for the coupled Kortewegde Vries
system and the generalized coupled variablecoefficient modified Kortewegde Vries
system. In addition to this, the conservation laws for the two systems are derived
using the multiplier approach and the conservation theorem due to Ibragimov.
Finally, a new coupled Kortewegde Vries system and a new coupled Kadomtsev
Petviashvili system are analyzed using Lie symmetry method. Exact solutions are
obtained using the Lie symmetry method in conjunction with the simplest equation,
Jacobi elliptic function and (G'/G)expansion methods. Conservation laws are also
obtained for both the systems by employing the multiplier approach. / Thesis (PhD.(Applied Mathematics) NorthWest University, Mafikeng Campus, 2013

2 
Tangent and cotangent bundles automorphism groups and representations of Lie groups /Hindeleh, Firas. January 2006 (has links)
Thesis (Ph.D.)University of Toledo, 2006. / Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 7982.

3 
Some aspects of formal lie groupsGeorgoudis, John. January 1968 (has links)
No description available.

4 
An infinitesimal approach to Lie groups and applicationsGould, Mark David January 1979 (has links)
1 v. (various paging) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.1980) from the Dept. of Mathematical Physics, University of Adelaide

5 
An infinitesimal approach to Lie groups and applications.Gould, Mark David. January 1979 (has links) (PDF)
Thesis (Ph.D. 1980) from the Department of Mathematical Physics, University of Adelaide.

6 
Die Geometrie Nilpotenter Liegruppen mit linksinvarianter MetrikSchubert, Matthias. January 1983 (has links)
Originally presented as author's thesis, Bonn, 1983. / Bibliography: p. 74.

7 
Some aspects of formal lie groupsGeorgoudis, John January 1968 (has links)
No description available.

8 
Symmetry reductions, exact solutions and conservation laws of a variable coefficient (2+1)dimensional zakharovkuznetsov equation / Letlhogonolo Daddy Moleleki.Moleleki, Letlhogonolo Daddy January 2011 (has links)
This research studies two nonlinear problems arising in mathematical physics. Firstly
the Kortewegde VricsBurgers equation is considered. Lie symmetry method is
used to obtain t he exact solutions of Kortewegde VriesBurgers equation. Also
conservation laws are obtained for this equation using the new conservation theorem.
Secondly, we consider the generalized (2+ 1)dimensional ZakharovKuznctsov (ZK)
equation of time dependent variable coefficients from the Lie grouptheoretic point
of view. We classify the Lie point symmetry generators to obtain the optimal system
of onedimensional subalgebras of t he Lie symmetry algebras. These subalgebras arc
then used to construct a number of symmetry reductions and exact groupinvariant
solutions of the ZK equation. We utilize the new conservation theorem to construct
the conservation laws of t he ZK equation. / Thesis (M. Sci in Applied Mathematics) NorthWest University, Mafikeng Campus, 2011

9 
Symmetries in general relativitySteele, John D. January 1989 (has links)
The purpose of this thesis is to study those nonflat spacetimes in General Relativity admitting high dimensional Lie groups of motions, homotheties, conformals and affines, and to prove a theorem on the relationship between the first three of these. The basic theories and notations of differential geometry are set up first, and a useful theorem on firstorder partial differential equations is proved. The concepts of General Relativity are introduced, spacetimes are defined and a brief account of the wellknown Petrov and Segre classifications is given. The interplay between these classifications and the isotropy structure of the various Lie groups is discussed as is the socalled 'Schmidt method'. Generalised p.p. waves are studied, with a special study of the subclass of generalised plane waves undertaken, many different characterisations of these latter are found and their admitted symmetries are completely described. Motions, homotheties and affines are considered. A survey of symmetries in Minkowski space, and a summary of known results on spacetimes with high dimensional groups of motions is given. The problem of rdimensional groups of homotheties is studied. The r 6 cases are completely resolved, and examples in the r = 5 cases are given. All examples of nonflat spacetimes admitting the maximal group of affines are displayed, correcting an error in the literature. The thesis ends with a proof of the BilyalovDefriseCarter theorem, which states that for any non conformally flat spacetime there is a conformally related metric for which the original group of conformals is a group of homotheties (motions if not conformal to generalised plane waves). The proof given does not use Bilyalov's analyticity assumption, and is more geometric than DefriseCarter. The maximum size of the conformal group for a given Petrov type is found. An appendix gives a brief account of some REDUCE routines used to check some algebraic manipulations.

10 
Two dimensional harmonic maps into lie groups.January 2000 (has links)
by Tsoi, Man. / Thesis submitted in: July 1999. / Thesis (M.Phil.)Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 5657). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.5 / Chapter 2  Preliminary  p.12 / Chapter 2.1  Lie Group and Lie Algebra  p.12 / Chapter 2.2  Harmonic Maps  p.15 / Chapter 2.3  Some Factorization theorems  p.17 / Chapter 3  A Survey on Unlenbeck's Results  p.22 / Chapter 3.1  Preliminary  p.24 / Chapter 3.2  Extended Solutions  p.26 / Chapter 3.3  The Variational Formulas for the Extended Solutions  p.30 / Chapter 3.4  "The Representation of A(S2, G) on holomorphic maps C* → G"  p.33 / Chapter 3.5  An Action of G) on extended solutions and Backlund Transformations  p.39 / Chapter 3.6  The Additional S1 Action  p.42 / Chapter 3.7  Harmonic Maps into Grassmannians  p.43 / Chapter 4  Harmonic Maps into Compact Lie Groups  p.47 / Chapter 4.1  Symmetry group of the harmonic map equation  p.48 / Chapter 4.2  A New Formulation  p.49 / Chapter 4.3  "Harmonic Maps into Grassmannian, Another Point of View"  p.53 / Bibliography

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