Complete Integrability and Discretization of Euler Top and Manakov Top

Author

Austin Marstaller, The University of Texas Rio Grande Valley

Date of Award

8-2020

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Baofeng Feng

Second Advisor

Dr. Elena Poletaeva

Third Advisor

Dr. Dambaru Bhatta

Abstract

The Euler top is a completely integrable system with physical system implications and the Manakov top is its four-dimensional extension. We are concerned about their complete integrability and the preservation of this property under a specific discretization known as the Hirota-Kimura Discretization. Surprisingly, it is not guaranteed that under any discretization the conserved quantities are preserved and therefore they must be discovered. In this work we construct the Poisson bracket and Lax pair for each system and provide the Lie algebra background needed to do such such constructions.

Comments

Copyright 2020 Austin Marstaller. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/complete-integrability-discretization-euler-top/docview/2495454535/se-2?accountid=7119

Recommended Citation

Marstaller, Austin, "Complete Integrability and Discretization of Euler Top and Manakov Top" (2020). Theses and Dissertations. 712.
https://scholarworks.utrgv.edu/etd/712