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

• 作者: Masatomo Matsushima Mayumi Ohmiya
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: KDV POLYNOMIALS MKDV (-) POLYNOMIALS Schr?dinger OPERATOR DIRAC OPERATOR
• 年，卷（期）: 2013,（1）
• 页码范围: 209-213
• 页数: 5页
• 分类号: O1

摘要

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.