Tanki Motsepa

Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

Symmetry Analysis and Conservation Laws of the Zoomeron Equation

In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the first time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the first time, we construct the conservation laws of the underlying equation using the multiplier method.

Conservation laws and solutions of a generalized coupled (2+1)-dimensional Burgers system

Abstract In this paper we study a generalized coupled (2+1)-dimensional Burgers system, which is a nonlinear version of a bilinear system under some dependent variable transformations. It was introduced recently in the literature and has attracted a fair amount of interest from physicists. The Lie symmetry analysis together with the Kudryashov approach are utilized to obtain new travelling wave solutions of the system. Furthermore, for the first time, conservation laws of the system are derived using the multiplier method.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

Abstract The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

A study of the Bona-Smith system describing the two-way propagation of water waves in a channel

We study a coupled system of equations, known as Bona-Smith system, which can be used to describe the two-way propagation of (one-dimensional) long waves of small but finite amplitude in an open channel of water of constant depth. Conservation laws are obtained using Noether’s method and furthermore we present exact solutions of the system.

A Study of an Extended Generalized (2+1)-dimensional Jaulent–Miodek Equation

Abstract This paper aims to study the extended generalized (2+1)-dimensional Jaulent–Miodek equation (egJM), which arises in a number of significant nonlinear problems of physics and applied mathematics. We derive conservation laws using Noether theorem and find travelling wave solution of the egJM equation.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

Abstract In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Solutions and conservation laws for a Kaup-Boussinesq system

In this work we study a Kaup-Boussinesq system, which is used in the analysis of long waves in shallow water. Travelling wave solutions are obtained by using direct integration. Secondly, conservation laws are derived by using the multiplier method.

Travelling wave solutions of a coupled Korteweg-de Vries-Burgers system

In this paper we study a coupled Korteweg-de Vries-Burgers system which arises in mathematical physics and has a wide range of scientific applications. We obtain new travelling wave solutions of this system by employing the (G’/G)-expansion method. The solutions that will be obtained are going to be expressed in two different forms, viz., hyperbolic functions and trigonometric functions.

Exact solutions and conservation laws for a generalized improved Boussinesq equation

In this paper we study a nonlinear generalized improved Boussinesq equation, which describes nonlinear dispersive wave phenomena. Exact solutions are derived by using the Lie symmetry analysis and the simplest equation methods. Moreover, conservation laws are constructed by using the multiplier method.