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Semi-Commutative Differential Operators Associated with the Dirac Opetator and Darboux Transformation
Doshisha University, Kyoto, Japan
Doshisha University, Kyoto, Japan
- 1 Doshisha University, Kyoto, Japan
- 2 Doshisha University, Kyoto, Japan
Advances in Pure Mathematics·Volume 03 (2013)·Pages 209–213·Published 30 January 2013·DOI10.4236/apm.2013.31A029
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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.
KeywordsKdV PolynomialsmKdV (-) PolynomialsSchrödinger OperatorDirac Operator
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