Date of Award:
8-2020
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Zhaohu Nie
Committee
Zhaohu Nie
Committee
Ian Anderson
Committee
Nathan Geer
Abstract
The Toda lattice is a famous integrable system studied by Toda in the 1960s. One can study the Toda lattice using a matrix representation of the system. Previous results have shown that this matrix of dimension n with 1 band and n‚àí1 bands is Liouville integrable. In this paper, we lay the foundation for proving the general case of the Toda lattice, where we consider the matrix representation with dimension n and a partially filled lower triangular part. We call this the banded Toda flow. The main theorem is that the banded Toda flow up to dimension 10 is Liouville integrable. To conclude the paper, we will present some conjectures which, we hope, will help us in proving the Liouville integrability of the banded Toda flow of dimension n with k number of bands.
Checksum
82ddab87d68c361555502df07b4864c5
Recommended Citation
Youmans, Zachary, "Some Examples of the Liouville Integrability of the Banded Toda Flows" (2020). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7804.
https://digitalcommons.usu.edu/etd/7804
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