Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches

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In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations and finding a contact transformation between the generalized Hunter-Saxton equation and the Euler-Poisson equation.
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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