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1 
Application of lie group methods to certain partial differential equations / Isaiah Elvis MhlangaMhlanga, Isaiah Elvis January 2012 (has links)
In the first part of this work, two nonlinear partial differential equations, namely, a
modified CamassaHolmDegasperisProcesi equation and the generalized Kortewegde Vries equation with two power law nonlinearities are studied. The Lie symmetry method along with the simplest equation method is used to construct exact Solutions for these two equations. The second part looks at two systems of partial
differential equations, namely, the generalized BoussinesqBurgers equations and the
(2+1)dimensional DaveyStewartson equations. The Lie symmetry method and the
travelling wave hypothesis approach are utilized to obtain exact solutions of the generalized BoussinesqBurgers equations. The travelling wave hypothesis approach is
used to find exact solutions of the (2+ 1 )dimensional DaveyStewartson equations. / Thesis (Msc. in Applied Mathematics) NorthWest University, Mafikeng Campus, 2012

2 
Über algebraische Eigenschaften von linearen homogenen DifferentialausdrückenBlumberg, Henry, January 1912 (has links)
Thesis (doctoral)GeorgAugustUniversität zu Göttingen, 1912. / Cover title. Vita. Includes bibliographical references.

3 
Ueber Fuchs'sche Differentialgleichungen vierten GradesKrause, August, January 1897 (has links)
Thesis (doctoral)FriedrichWilhelmsUniversität zu Berlin, 1897. / Vita. Includes bibliographical references.

4 
Über lineare homogene Differentialgleichungen zweiter Ordnung, welche Integrale besitzen, durch deren Umkehrung sich eindeutige Funktionen zweier Variablen ergebenLohnstein, Rudolf, January 1890 (has links)
Thesis (doctoral)FriedrichWilhelmsUniversität zu Berlin, 1890. / Vita. Includes bibliographical references.

5 
Surfaces associated with a congruenceGore, Greenville D., January 1932 (has links)
Thesis (Ph. D.)University of Chicago. / Vita. "Private edition distributed by the University of Chicago libraries, Chicago, Illinois."

6 
The integrability of the differential equation representing the sum of a family of seriesO'Shaughnessy, Louis. January 1912 (has links)
Thesis (Ph. D.)University of Pennsylvania, 1911. / Vita.

7 
Meromorphic solutions of complex differential equationsWu, Chengfa, 吳成發 January 2014 (has links)
The objective of this thesis is to study meromorphic solutions of complex algebraic ordinary differential equations (ODEs). The thesis consists of two main themes. One of them is to find explicitly all meromorphic solutions of certain class of complex algebraic ODEs. Since constructing explicit solutions of complex ODEs in general is very difficult, the other theme (motivated by the classical conjecture proposed by Hayman in 1996) is to establish estimations on the growth of meromorphic solutions in terms of Nevanlinna characteristic function.
The tools from complex analysis that will be used have been collected in Chapter 1. Chapter 2 is devoted to introducing a method, which was first used by Eremenko and later refined by Conte and Ng, to give a classification of some complex algebraic autonomous ODEs. Under certain assumptions, based on local singularity analysis and Nevanlinna theory, this method shows that all meromorphic solutions of these ODEs if exist, must belong to ‘class W’, which consists of elliptic functions and their degenerations. Combined with knowledge from function theory, as shown by Demina and Kudryashov, it further allows us to find all of them explicitly and the details of the method will be illustrated by constructing new real meromorphic solutions of the stationary case of cubicquintic SwiftHohenberg equation. In Chapter 3, the same method is used to construct on R^n, n ≥ 2 some explicit Bryant solitons and on R^n\{0}, n ≥ 2 some Ricci solitons, and one of them turns out to be a new Ricci soliton on R^5\{0}. In addition, the completeness of corresponding metrics on the Ricci solitons that we have constructed are also discussed.
In 1996, Hayman conjectured an upper bound on the growth, in terms of Nevanlinna characteristic function, of meromorphic solutions of complex algebraic ODEs. Related work in the literature towards this socalled classical conjecture is first reviewed in Chapter 4. The classical conjecture for three types of second order complex algebraic ODEs will then be verified by either giving a classification of the meromorphic solutions or obtaining them explicitly in Chapter 4. As the classical conjecture seems to be out of reach at present, we proposed in Chapter 5 to study a particular class of complex algebraic ODEs which can be factorized into certain form. On one hand, for these factorizable ODEs, it has been proven for the generic case that all their meromorphic solutions must be elliptic functions or their degenerations. On the other hand, the second order factorizable ODEs have been carefully studied so that their meromorphic solutions have been obtained explicitly except one case. This will allow the classical conjecture for most of the second order factorizable ODEs to be verified by employing Nevanlinna theory and certain qualitative results from complex differential equations. Finally, the classical conjecture has been shown to be sharp in certain cases. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

8 
Singular perturbation problems of ordinary differential equationsGangal, Mahendra Kumar. January 1968 (has links)
No description available.

9 
Bifurcation in periodic differential equations and the twovariable method.Gentile, Francesco January 1973 (has links)
No description available.

10 
Certain aspects of the stability of solutions of systems of nonlinear differential equationsStubbs, Robert Taylor 05 1900 (has links)
No description available.

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