Exact Solutions of Einstein's Field Equations

Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wavelike behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term r...

Exact Solutions of Einstein’s Field Equations

We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with the pressure, and (ii)...

Exact solutions of nonlinear interval Volterra integral equations

Exact solutions of (3 +1)-dimensional nonlinear evolution equations

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

Exact Solutions for Nonlocal Nonlinear Field Equations in Cosmology

A method for the search of exact solutions for equation of a nonlocal scalar field in a non-flat metric is considered. In the Friedmann–Robertson–Walker metric the proposed method can be used in the case of an arbitrary potential, with the exception of linear and quadratic potentials, and allows to get in quadratures solutions, which depend on two arbitrary parameters. Exact solutions have been...