Embedding algorithms and applications to differential equations. (May 2018)

• Record Type: Journal Article
• Authors: Ali, Sajid; Azad, Hassan; Biswas, Indranil; Ghanam, Ryad; Mustafa, M.T.
• Is Part Of: Journal of symbolic computation. Volume 86(2018)
• Page Start: 166
• Page End: 188
• Publication Date: 2018-05
• Subjects: 17B45 -- 17B30 -- 17B81 -- 34L99; Maximal solvable subalgebras -- Algebraic Lie algebras -- Invariant solutions; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.05.002
• Languages: English
• ISSNs: 0747-7171

Abstract

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.