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Application of lie group methods to certain partial differential equations
(2012)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 ... 
Conservation laws and exact solutions for some nonlinear partial differential equations
(NorthWest University (South Africa), 2016)In this thesis we study some nonlinear partial diffrerential equations which appear in several physical phenomena of the real world. Exact solutions and conservation laws are obtained for such equations using various ... 
Conserved quantities, optimal systems and explicit solutions of certain partial differential equations
(NorthWest University (South Africa), 2021)In this thesis we study nine nonlinear partial differential equations (NLPDEs) from the point of view of classical Lie point symmetries and conserved quantities. These equations of choice have real world applications, ... 
Conserved vectors and analytic solutions of potential KadomtsevPetviashvili and Kortewegde Vrieslike equations
(NorthWest University (South Africa), 2023)In this work, we study three nonlinear partial differential equations that are used to simulate a variety of physical processes in science. As an example of what will be done in this dissertation, we start off by looking ... 
Conserved vectors, symmetry reductions and solutions for some nonlinear partial differential equations
(NorthWest University (South Africa), 2022)In this thesis, Lie group analysis is utilized to examine a number of higherorder nonlinear partial differential equations (NPDEs). Additionally, conserved vectors for these NPDEs are derived. The equations addressed ... 
Exact solutions and conversation laws of (2+1)  dimensional zarkharovkuznetsov modified equal width equation
(NorthWest University, 2011)In this dissertation exact solutions of the (2+1) dimensional ZakharovKuznetsov modified equal width equation arc obtained. The Lie group analysis is used to carry out the integration of this equation. The solutions ... 
Group Classification of a General BondOption Pricing Equation
(2013)The main purpose of this work is to perform the Lie group classification of a general bondoption pricing equation. The procedure involves finding the Lie symmetries of the said partial differential equation and employing ... 
Invariant solutions and conservation laws for soil water redistribution and extraction flow models
(2003)In this dissertation we use Lie symmetry analysis to obtain invariant solutions for certain soil water equations. These solutions are invariant under twoparameter symmetry groups obtained by the group classification of ... 
Lie group analysis of certain nonlinear differential equations arising in fluid mechanics
(NorthWest University, 2010)This research studies two nonlinear differential equations arising in fluid mechanics. Firstly, the ZakharovKuznetsov's equation in (3+1) dimensions with an arbitrary power law nonlinearity is considered. The method of ... 
Lie group analysis of the new extended KP and threedimensional KPBBM equations
(NorthWest University (South Africa), 2023)In this dissertation, we examine three partial deferential equations that are nonlin ear. Namely, nonlinear filtration equation, the new extended KadomtsevPetviashvili equation (eKP) and the KadomtsevPetviashviliBenj ... 
Lie symmetry analysis of certain nonlinear evolution equations of mathematical physics
(2013)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 ... 
A study of a generalized potential YuTodaSasa Fukuyama and fifthorder nonlinear partial differential equations
(NorthWest University (South Africa), 2023)In this work we study two nonlinear partial differential equations which arise in mathematical physics. These equations have been studied in the literature. However, we start by considering a secondorder nonlinear ... 
A study of certain multidimensional partial differential equations using Lie symmetry analysis
(NorthWest University (South Africa), 2019)In this thesis we study certain nonlinear multidimensional partial differential equations which are mathematical models of various physical phenomena of the real world. Closedform solutions and conservation laws are ... 
A study of equalwidth and ZakharovKuznetsovBurgers equations
(NorthWest University (South Africa), 2019)In this work we study some nonlinear partial differential equations which evolve in mathematical physics and other fields of science. We start by considering a secondorder nonlinear Burgers equation as an illustration of ... 
Symmetry analysis of modified equalwidth and nonlinear advectiondiffusion equations
(NorthWest University (South Africa), 2019)In this work we examine two nonlinear partial diﬀerential equations of ﬂuid mechanics. The modiﬁed equalwidth (MEW) equation, which is used in handling the simulation of a single dimensional wave propagation in nonlinear ... 
Symmetry reductions, exact solutions and conservation laws of a variable coefficient (2+1)dimensional zakharovkuznetsov equation
(2011)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 ...