# B\"acklund transformations for the nonholonomic Veselova system

## TL;DR

This paper develops Bäcklund transformations for the Veselova nonholonomic system, revealing new integrable systems on the sphere with higher-order polynomial integrals, advancing the understanding of nonholonomic integrability.

## Contribution

It introduces auto and hetero Bäcklund transformations for the Veselova system using divisor arithmetic on a genus two hyperelliptic curve, a novel approach in this context.

## Key findings

- Derived Bäcklund transformations for the Veselova system.
- Identified new integrable systems on the sphere with fourth-order polynomial integrals.
- Enhanced the mathematical framework for nonholonomic integrability.

## Abstract

We present auto and hetero B\"acklund transformations of the nonholonomic Veselova system using standard divisor arithmetic on the hyperelliptic curve of genus two. As a by-product one gets two natural integrable systems on the cotangent bundle to the unit two-dimensional sphere whose additional integrals of motion are polynomials in the momenta of fourth order.