Ahmad T. Ali

Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility

The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.

Some invariant string cosmological models in cylindrically symmetric space-time

In this paper we derive some new invariant solutions of Einstein-Maxwells field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and eometrical properties of the models derived in the paper. The solutions, at least one of them, are interesting physically as they can explain the accelerating as well as singularity free Universe.

Symmetry Group Analysis for Perfect Fluid Inhomogeneous Cosmological Models in General Relativity

In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. For this, Lie group analysis is used to identify the generator (isovector fields) that leave the given system of PDEs (Einstein’s field equations) invariant for the models under consideration. A new class of exact solutions of Einstein’s field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail.

Intrinsic Equations of Some Special Curves in Euclidean 3-Space

Abstract In this paper, we obtain the intrinsic equations of some special curves in Euclidean 3-space characterized by det = 0, where r i < r i+1,r 1 ∈ {1, 2, 3}, r 2 ∈ {2, 3, 4} and r 3 ∈ {3, 4, 5}.

Time-Like Smarandache Curves Derived from a Space-Like Helix

Abstract A regular curve in Minkowski space-time , whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache curve. We define a special case of such curves and call it Smarandache TB2 curves in the Minkowski space-time . Moreover, we compute formulas of its Frenet apparatus according to base curve via the method expressed in [5, 6]. By this way, we obtain another orthonormal frame of a such curve in .