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Semi-Commutative Differential Operators Associated with the Dirac Opetator and Darboux Transformation

Author(s): Masatomo Matsushima | Mayumi Ohmiya

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 01;
Start page: 209;
Date: 2013;
Original page

Keywords: KdV Polynomials | mKdV (-) Polynomials | Schrödinger Operator | Dirac Operator

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.
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