# Geometric Algorithm of Schr\"odinger Flow on a Sphere

## TL;DR

This paper develops an explicit geometric algorithm to solve the periodic Schr"odinger flow on a sphere, providing a constructive approach to the problem with both theoretical and experimental validation.

## Contribution

It introduces a novel explicit construction method for solutions to the Schr"odinger flow on a sphere, enabling a geometric algorithm for the periodic Cauchy problem.

## Key findings

- Explicit solution construction for Schr"odinger flow on a sphere
- Development of a geometric algorithm for the periodic Cauchy problem
- Theoretical and experimental validation of the method

## Abstract

We construct the solution to the periodic Cauchy problem of the Schr\"odinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric algorithm of solving this periodic Cauchy problem follows. Theoretical and experimental results will be discussed.