Very few exact solutions are known for the non-linear Vialov ordinarydifferential equation describing the longitudinal profiles of alpine glaciersand ice caps under the assumption that the ice deforms according to Glen'sconstitutive relationship. Using a simple, yet wide, class of models for theaccumulation rate of ice and Chebysev's theorem on the integration of binomialdifferentials, many new exact solutions of the Vialov equations are obtained interms of elementary functions.
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