https://doi.org/10.1140/epjp/s13360-020-00909-4
Regular Article
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
* e-mail: vfaraoni@ubishops.ca
Received:
30
September
2020
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
