Lagrangian formulation, a general relativity analogue, and a symmetry of the Vialov equation of glaciology
Department of Physics and Astronomy, Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada
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Accepted: 31 October 2020
Published online: 5 November 2020
Using a suitable rescaling of the independent variable, a Lagrangian is found for the nonlinear Vialov equation ruling the longitudinal profiles of glaciers and ice caps in the shallow ice approximation. This leads to a formal analogy between the (rescaled) Vialov equation and the Friedmann equation of relativistic cosmology, which is explored. This context provides a new symmetry of the (rescaled) Vialov equation and gives, at least formally, all its solutions using a generating function, which is the Nye profile for the degenerate case of perfectly plastic ice.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020