Date of Award:

8-2020

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

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

Included in

Mathematics Commons

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