5 research outputs found
An Algorithm to Determine Potential Systems in Mathematica
AbstractA symmetry analysis of differential equations plays an important role in discovering new solutions. In this article potential symmetries characterized by nonlocal transformations are introduced and an algorithm implemented in the computer algebra system Mathematica is presented which determines automatically potential systems and the corresponding potential symmetries. The possibilities of this algorithm are discussed by the examples of a nonlinear telegraph equation and the axial symmetric wave equation
Two-Component Dust in Spherically Symmetric Motion
Two components of spherically symmetric, inhomogeneous dust penetrating each
other are introduced as a generalization of the well-known Tolman-Bondi dust
solution. The field equations of this model are formulated and general
properties are discussed. inhomogeneous Special solutions with additional
symmetries - an extra Killing- or homothetic vector - and their matching to the
corresponding Tolman-Bondi solution are investigated.Comment: 16 pages, LaTeX, 5 figures, accepted for publication in Class.
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