Semi-Commutative Differential Operators Associated with the Dirac Opetator and Darboux Transformation ()
Affiliation(s)
ABSTRACT
In the present paper, the semi-commutative differential oparators associated with the 1-dimensional Dirac operator are constructed. Using this results, the hierarchy of the mKdV (-) polynomials are expressed in terms of the KdV polynomials. These formulas give a new interpretation of the classical Darboux transformation and the Miura transformation. Moreover, the recursion operator associated with the hierarchy of the mKdV (-) polynomials is constructed by the algebraic method.
KEYWORDS
Share and Cite:
Copyright © 2024 by authors and Scientific Research Publishing Inc.
This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.