Share This Article:

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

Full-Text HTML XML Download Download as PDF (Size:129KB) PP. 209-213
DOI: 10.4236/apm.2013.31A029    3,633 Downloads   6,312 Views

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.

Cite this paper

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.

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.