This textbook comprehensively introduces scholars and researchers to the appliance of constant symmetries and their Lie algebras to bland and partial differential equations. overlaying the entire glossy innovations intimately, it relates purposes to state of the art learn fields resembling Yang turbines conception and string conception. geared toward readers in utilized arithmetic and physics instead of natural arithmetic, the fabric is very best to scholars and researchers whose major curiosity lies to find recommendations to differential equations and invariants of maps. a great number of labored examples and not easy workouts support readers to paintings independently of academics, and by way of together with SymbolicC++ implementations of the innovations in each one bankruptcy, the e-book takes complete benefit of the developments in algebraic computation. Twelve new sections were further during this version, together with: Haar degree, Sato's thought and sigma services, common algebra, anti-self twin Yang turbines equation, and discrete Painlevé equations.

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