Embedding algorithms and applications to differential equations. (May 2018) - Ali, Sajid; Azad, Hassan; Biswas, Indranil; Ghanam, Ryad; Mustafa, M.T.
Abstract: Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the symmetry algebra of the wave equation, which in turn are used to determine a large class of invariant solutions of the wave equation. The algorithms are also illustrated for the symmetry algebra of a classical system of differential equations considered by Cartan in the context of contact geometry.