Introduction to Symmetry Analysis

By Brian J. Cantwell, TH Moulden. 2002

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Differential invariant algebras of Lie pseudo-groups (2009, background): “[20], conformal geometry and conformal field theory, [16, 18], symplectic and Poisson geometry, [36, 40], and the geometry of real hypersurfaces, [11], as well as symmetry groups of a wide variety of partial differential equations, [28, 40], gauge theories, [4], fluid mechanics, [2, 7], solitons and”
Particle-size segregation and diffusive remixing in shallow granular avalanches (2006, background): “The concentration mapping has transformed the segregation–remixing equation (5.3) into the Burgers equation (5.7), whose properties are well known (e.g. Whitham 1974; Billingham & King 2000; Cantwell 2002).”
Maurer–Cartan forms and the structure of Lie pseudo-groups (2005, background): “Lie pseudo-groups appear in many fundamental physical and geometrical contexts, including gauge symmetries, [6], Hamiltonian mechanics and symplectic and Poisson geometry, [54], conformal geometry of surfaces and conformal field theory, [20, 23], the geometry of real hypersurfaces, [17], symmetry gr”
Moving Frames for Lie Pseudo–Groups (2008, background): “A particularly important case is when the pseudo-group represents the symmetry group of a system of differential equations and the submanifolds are the graphs of candidate solutions [7, 47].”