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11.
This article has a dual purpose: i) to provide a flavor of the scientific highlights of the landmark conference, GR3, held in July 1962 at Jablonna, near Warsaw; and, ii) to present a bird’s eye view of the tremendous advances that have occurred over the half century that separates GR3 and GR20, which was again held in Warsaw in July 2013. 相似文献
12.
K. S. Govinder P. G. L. Leach S. D. Maharaj 《International Journal of Theoretical Physics》1995,34(4):625-639
In 1987 C. C. Dyer, G. C. McVittie, and L. M. Oattes derived the (two) field equations for shear-free, spherically symmetric perfect fluid spacetimes which admit a conformai symmetry. We use the techniques of the Lie and Painlevé analyses of differential equations to find solutions of these equations. The concept of a pseudo-partial Painlevé property is introduced for the first time which could assist in finding solutions to equations that do not possess the Painlevé property. The pseudo-partial Painlevé property throws light on the distinction between the classes of solutions found independently by P. Havas and M. Wyman. We find a solution for all values of a particular parameter for the first field equation and link it to the solution of the second equation. We indicate why we believe that the first field equation cannot be solved in general. Both techniques produce similar results and demonstrate the close relationship between the Lie and Painlevé analyses. We also show that both of the field equations of Dyeret al. may be reduced to the same Emden-Fowler equation of index two. 相似文献
13.
We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically
symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms
of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously
with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised
geometrically by a conformal Killing vector. 相似文献
14.
N.C. Caister K.S. Govinder J.G. O’Hara 《Nonlinear Analysis: Real World Applications》2011,12(4):2408-2415
We provide group invariant solutions to two nonlinear differential equations associated with the valuing of real options with utility pricing theory. We achieve these through the use of the Lie theory of continuous groups, namely, the classical Lie point symmetries. These group invariant solutions, constructed through the use of the symmetries that also leave the boundary conditions invariant, are consistent with the results in the literature. Thus it may be shown that Lie symmetry algorithms underlie many ad hoc methods that are utilised to solve differential equations in finance. 相似文献
15.
We present a simple nonstatic generalization of the isothermal universe. The cosmological fluid obeys a barotropic equation of state of the form p=. We employ a causal heat transport equation of the Maxwell–Cattaneo form to study the thermodynamical behavior of our model. 相似文献
16.
A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions. 相似文献
17.
We investigate the effect of heat dissipation in inhomogeneous cosmologies by invoking the full causal theory of heat transport within the framework of extended irreversible thermodynamics. This work extends earlier results which were obtained using the truncated causal heat transport equation. In particular, we show that the truncation of the heat transport equation implicitly defines a temperature law which leads to pathological behaviour in the temperature of the evolving cosmic fluid. 相似文献
18.
New exact solutions of a generalised Boussinesq equation with damping term and a system of variant Boussinesq equations via double reduction theory
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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
19.
In this paper we revisit the problem of modeling radiating stars in which the areal radius is equal to the proper radius throughout
the stellar evolution. We provide a new family of solutions that completely describes the dynamical behaviour of these so-called
Euclidean stars. The solution satisfies all the energy conditions, and importantly, admits a barotropic equation of state. 相似文献
20.
We analyze a class of third‐order evolution equations, i.e. ut = f(x, ux, uxx) uxxx+g(x, ux, uxx) via the method of preliminary group classification. This method is a systematic means of analyzing the equation for symmetries. We find explicit forms of f and g, which allow for a larger dimensional Lie algebra of point symmetries. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献