Date of Award:
Master of Science (MS)
Mathematics and Statistics
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−1 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.
Youmans, Zachary, "Some Examples of the Liouville Integrability of the Banded Toda Flows" (2020). All Graduate Theses and Dissertations. 7804.
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