Darboux tranformation and solutions of some integrable systems
Dolores Barrios Rolania
TL;DR
This paper explores how Darboux transformations can generate solutions for integrable systems, specifically extending results to more general matrix cases using the discrete KdV equation.
Contribution
It extends the connection between Darboux transformations and solutions of the Kostant Toda lattice to general (p+2)-banded Hessenberg matrices.
Findings
Extended Darboux transformation solutions to general (p+2)-banded Hessenberg matrices.
Linked Darboux transformations with solutions of the full Kostant Toda lattice.
Utilized discrete KdV equation to derive new solutions.
Abstract
The relation between the Darboux transformation and the solutions of the full Kostant Toda lattice is analyzed. The discrete Korteweg de Vries equation is used to obtain such solutions and the main result of [1] is extended to the case of general (p + 2)-banded Hessenberg matrices.
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