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21.
New exact solutions of a generalised Boussinesq equation with damping term and a system of variant Boussinesq equations via double reduction theory 下载免费PDF全文
Justina Ebele Okeke Rivendra Narain Kesh Sathasiva Govinder 《Journal of Applied Analysis & Computation》2018,8(2):471-485
The conservation laws of a generalised Boussinesq (GB) equation with damping term are derived via the partial Noether approach. The derived conserved vectors are adjusted to satisfy the divergence condition. We use the definition of the association of symmetries of partial differential equations with conservation laws and the relationship between symmetries and conservation laws to find a double reduction of the equation. As a result, several new exact solutions are obtained. A similar analysis is performed for a system of variant Boussinesq (VB) equations. 相似文献
22.
N. C. Caister K. S. Govinder J. G. O'Hara 《Mathematical Methods in the Applied Sciences》2011,34(11):1353-1365
Asian options are useful financial products as they guard against large price manipulations near the termination date of the contract. In addition, they are often cheaper than their vanilla European counterparts. Previous analyses of the Asian option partial differential equation (PDE) have obtained analytical solutions for the fixed strike (arithmetically averaged) Asian option (and then only with certain assumptions on the boundary conditions). Using Lie symmetry analysis we obtain an optimal system of Lie point symmetries and demonstrate that many (usually ad hoc) reductions of the Asian option PDE are contained in this minimal set. We analyse each reduction member and the feasibility of its resulting invariant solution with the boundary conditions. We show that the numerical simulations on a reduced equation are more efficient than on the original specified problem. In addition, we have found new analytical solutions in terms of Fourier transforms for the floating strike Asian option as well as the fixed strike Asian option without the simplification of the domain. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
23.
In the search for solutions to the important partial differential equation due to Black, Scholes and Merton potential symmetries are very useful as new solutions of the equation can be obtained as a result. These potential symmetries require that the equation be written in conserved form, ie. we need to determine conservation laws for the equation. We calculate the conservation laws utilizing the point symmetries of the equation following the method of Kara and Mahomed [A.H. Kara, F.M. Mahomed, The relationship between symmetries and conservation laws, Int. J. Theor. Phys. 39 (2000) 23–40]. 相似文献
24.
Barbara Abraham-Shrauner Keshlan S. Govinder 《Journal of Mathematical Analysis and Applications》2008,343(1):525-530
An approach for determining a class of master partial differential equations from which Type II hidden point symmetries are inherited is presented. As an example a model nonlinear partial differential equation (PDE) reduced to a target PDE by a Lie symmetry gains a Lie point symmetry that is not inherited (hidden) from the original PDE. On the other hand this Type II hidden symmetry is inherited from one or more of the class of master PDEs. The class of master PDEs is determined by the hidden symmetry reverse method. The reverse method is extended to determine symmetries of the master PDEs that are not inherited. We indicate why such methods are necessary to determine the genesis of Type II symmetries of PDEs as opposed to those that arise in ordinary differential equations (ODEs). 相似文献
25.
Nyonyi Y. Maharaj S. D. Govinder K. S. 《The European Physical Journal C - Particles and Fields》2013,73(11):1-9
The European Physical Journal C - We study shear-free spherically symmetric relativistic gravitating fluids with heat flow and electric charge. The solution to the Einstein–Maxwell system is... 相似文献
26.
We investigate the integrability of cosmic strings in Bianchi III spacetime using a symmetry analysis. The behaviour of the
model is reduced to the solution of a single second order nonlinear differential equation. We show that this equation has
a rich structure and admits an infinite family of solutions. Our class of solutions extends special cases previously obtained
by Tikekar and Patel [Gen. Relativ. Gravit.
24, 397 (1992)]. 相似文献
27.
Vishnu J. Ram Hrishi Kesh Pandey Arnold J. Vlietinck 《Journal of heterocyclic chemistry》1981,18(1):55-57
A series of 6,7-phenanthreno- and 6,7-acenaphthenopteridines bearing different substituents at positions 2 and 4 are prepared. The structures of the compounds are confirmed by spectroscopic studies and elemental analyses. 相似文献
28.
In this study, we consider a mathematical model of two competing prey and one predator system where the prey species follow Lotka–Volterra‐type dynamics and the predator uptake functions are ratio dependent. We have derived the conditions for existence of different boundary equilibria and discussed their global behaviour. The sufficient condition for permanent co‐existence of all the species is derived. Finally, we have discussed the possibility of extinction of the species from the system. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
29.
G. Z. Abebe K. S. Govinder S. D. Maharaj 《International Journal of Theoretical Physics》2013,52(9):3244-3254
We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial differential equation. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analysed. We identify new categories of exact solutions to the boundary conditions. Two classes of solutions are of interest. The first class depends on a self similar variable. The second class is separable in the spacetime variables. 相似文献
30.
M. Govender K. S. Govinder D. Fleming 《International Journal of Theoretical Physics》2012,51(11):3399-3409
We analyse a new family of solutions to the Einstein field equations describing the collapse of a fluid sphere in the presence of heat flux and shear. These solutions ensure that the collapsing fluid is accelerating and provide a generalisation of the geodesic fluid models studied in earlier treatments. In particular, we demonstrate the role played by pressure in the dynamics of the collapse process. 相似文献