Exact solutions of Einstein's equations with ideal gas sources

Reduction and Exact Solutions of the Ideal Magnetohydrodynamic Equations

In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the classification by conjugacy classes of r-dimensional subalgebras (1 ≤ r ≤ 4) was already known. So we restrict our study to the three-dimensional Galilean-similitude su...

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 of Linear Equations with Rational

1. Introduction. Sometimes one is interested in exact solutions of linear equations and cannot tolerate any errors at all, be it round-off errors, truncation errors or otherwise. In such situations division cannot be used. Eliminating variables by cross-multiplying leads to a tremendous growth in the size of intermediate results. This is well illustrated in an example of J. Barkley Rosser [5], ...

Exact annihilating-ideal graph of commutative rings

The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.