Semi-Commutative Differential Operators Associated with the Dirac Opetator and Darboux Transformation ()
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.
Share and Cite:
M. Matsushima and M. Ohmiya, "Semi-Commutative Differential Operators Associated with the Dirac Opetator and Darboux Transformation,"
Advances in Pure Mathematics, Vol. 3 No. 1A, 2013, pp. 209-213. doi:
10.4236/apm.2013.31A029.
Conflicts of Interest
The authors declare no conflicts of interest.
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