# Solving the Vialov equation of glaciology in terms of elementary functions

## TL;DR

This paper derives many new exact solutions to the Vialov equation in glaciology using elementary functions, expanding the limited set of known solutions for glacier profile modeling.

## Contribution

It introduces a novel application of Chebyshev's theorem to find elementary solutions for the Vialov equation, broadening analytical tools in glaciology.

## Key findings

- Many new exact solutions derived
- Solutions expressed in elementary functions
- Enhanced understanding of glacier profile equations

## Abstract

Very few exact solutions are known for the non-linear Vialov ordinary differential equation describing the longitudinal profiles of alpine glaciers and ice caps under the assumption that the ice deforms according to Glen's constitutive relationship. Using a simple, yet wide, class of models for the accumulation rate of ice and Chebysev's theorem on the integration of binomial differentials, many new exact solutions of the Vialov equations are obtained in terms of elementary functions.