Supersymmetric quantum mechanics and the Korteweg-de Vries hierarchy
Aaron K. Grant, Jonathan L. Rosner
TL;DR
This paper explores how supersymmetric quantum mechanics can be used to derive conservation laws and construct the tau-function for the Korteweg-de Vries hierarchy, providing new insights into integrable systems.
Contribution
It demonstrates the role of supersymmetric quantum mechanics in deriving KdV conservation laws and understanding the Miura transformation, offering a novel approach to integrable systems analysis.
Findings
Supersymmetric quantum mechanics aids in deriving KdV conservation laws.
Provides insight into the Miura transformation.
Constructs the tau-function using supersymmetric methods.
Abstract
The connection between supersymmetric quantum mechanics and the Korteweg- de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the -function by means of supersymmetric quantum mechanics is discussed.
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