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M. Matsushima and M. Ohmiya, “An Algebraic Construction of the First Integrals of the Stationary KdV Hierarchy,” Proceeding of ICNAAM: Numerical Analysis and Applied Mathematics, Vol. 1, 2009, pp. 168-172.

has been cited by the following article:

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

  AUTHORS: Masatomo Matsushima, Mayumi Ohmiya

  KEYWORDS: KdV Polynomials; mKdV (-) Polynomials; Schrödinger Operator; Dirac Operator

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.1A, January 30, 2013

  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.