Abstract:
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.
Keywords:
Lie pseudo-groups; Maurer–Cartan forms; structure equations;symmetries of differential equations.
Received:August 8, 2005; in final form September 29, 2005; Published online October 13, 2005
\Bibitem{Mor05}
\by O.~I.~Morozov
\paper Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches
\jour SIGMA
\yr 2005
\vol 1
\papernumber 006
\totalpages 14
\mathnet{http://mi.mathnet.ru/sigma6}
\crossref{https://doi.org/10.3842/SIGMA.2005.006}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2173593}
\zmath{https://zbmath.org/?q=an:1092.58017}
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This publication is cited in the following 13 articles:
Denis Blackmore, Yarema Prykarpatsky, Mykola M. Prytula, Denys Dutykh, Anatolij K. Prykarpatski, “On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries”, Anal.Math.Phys., 12:2 (2022)
Morozov O.I., “Integrability Structures of the Generalized Hunter-Saxton Equation”, Anal. Math. Phys., 11:2 (2021), 50
Olver P., “Recent advances in the theory and application of lie pseudo-groups”, XVIII International Fall Workshop on Geometry and Physics, AIP Conference Proceedings, 1260, 2010, 35–63
Olver P.J., Pohjanpelto J., “Differential invariant algebras of Lie pseudo-groups”, Advances in Mathematics, 222:5 (2009), 1746–1792
Olver P.J., Pohjanpelto J., “Moving Frames for Lie Pseudo-Groups”, Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 60:6 (2008), 1336–1386
Olver P.J., Pohjanpelto J., “Pseudo-Groups, Moving Frames, and Differential Invariants”, IMA Volumes in Mathematics and its Applications, 144 (2008), 127–149
Morozov, OI, “Coverings of differential equations and Cartan's structure theory of Lie pseudo-groups”, Acta Applicandae Mathematicae, 99:3 (2007), 309
Olver P.J., Pohjanpelto J., “Differential Invariants for Lie Pseudo-Groups”, Grobner Bases in Symbolic Analysis, Radon Series on Computational and Applied Mathematics, 2, eds. Rosenkranz M., Wang D., Walter de Gruyter, 2007, 217–243
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