Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Exact Solutions of Einstein's Field Equations: Notation

THE number of systematic treatises on relativity is not unduly large. This is partly because, since the first few years after Einstein's announcement of the 'general' theory in 1917, it has undergone no fundamental development, and partly because the early expositions were so good. One cannot forbear mentioning those of Eddington, von Laue, Pauli, and Weyl. But these were addressed mainly to professionals, and, in spite of subsequent accounts from various points of view, there is still room for a plain text-book suitable for undergraduates reading relativity as a special subject, or for research students needing a working knowledge of it. Prof. Bergmann's book is designed to meet such requirements. Introduction to the Theory of Relativity By Prof. Peter Gabriel Bergmann. (Prentice-Hall Physics Series.) Pp. xvi + 287. (New York: Prentice-Hall, Inc., 1942.) 4.50 dollars.

Introduction to the Theory of Relativity

This paper obtains soliton solutions to optical couplers by two methods. These are sine–cosine function method and Bernoulli’s equation approach. There are four laws that are touched upon in this paper. These are Kerr law, power law, parabolic law and dual-power law. The first integration scheme is applicable to Kerr and power laws only where bright soliton solutions are retrievable. The second tool is applicable to parabolic and dual-power laws only that leads to dark and singular solitons for these two nonlinear media.

Optical solitons in nonlinear directional couplers by sine–cosine function method and Bernoulli’s equation approach

Lie symmetry analysis to the time fractional generalized fifth-order KdV equation

In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (G′/G)-expansion method, where G = G(ξ) satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.

Coupled Higgs field equation and Hamiltonian amplitude equation: Lie classical approach and (G′/G)-expansion method

An investigation of Lie point symmetries for systems of time fractional partial differential equations including Ito system, coupled Burgers equations, coupled Korteweg de Vries equations, Hirota-Satsuma coupled KdV equations, and coupled nonlinear Hirota equations has been done. Using the obtained symmetries, each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving Erdelyi-Kober fractional differential operator depending on a parameter α.

On invariant analysis of some time fractional nonlinear systems of partial differential equations. I

In this paper, variable coefficients Kawahara equation (VCKE) and variable coefficients modified Kawahara equation (VCMKE), which arise in modeling of various physical phenomena, are studied by Lie group analysis. The similarity reductions and exact solutions are derived by determining the complete sets of point symmetries of these equations. Moreover, some exact analytic solutions are considered by the power series method. Further, a generalized -expansion method is applied to VCKE and VCMKE for constructing some new exact solutions. As a result, hyperbolic function solutions, trigonometric function solutions and some rational function solutions with parameters are furnished. Copyright © 2012 John Wiley & Sons, Ltd.

Kawahara equation and modified Kawahara equation with time dependent coefficients: symmetry analysis and generalized G′G-expansion method

Painlevé analysis, Lie symmetries and exact solutions for (2+1)-dimensional variable coefficients Broer–Kaup equations

The symmetry method is developed to study space–time fractional nonlinear partial differential equations. Also, the Noether operators are extended for determining the conservation laws by application to some physically significant space–time fractional nonlinear partial differential equations.

R. K. Gupta

Papers

Coupled Higgs field equation and Hamiltonian amplitude equation: Lie classical approach and (G′/G)-expansion method

On invariant analysis of some time fractional nonlinear systems of partial differential equations. I

Kawahara equation and modified Kawahara equation with time dependent coefficients: symmetry analysis and generalized G′G-expansion method

Painlevé analysis, Lie symmetries and exact solutions for (2+1)-dimensional variable coefficients Broer–Kaup equations

Space–time fractional nonlinear partial differential equations: symmetry analysis and conservation laws