R. M. Miura, “Korteweg—De Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation,” Journal of Mathematical Physics, Vol. 9, No. 8, 1968, pp. 1202-1204. doi10.1063/1.1664700 - References

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R. M. Miura, “Korteweg—De Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation,” Journal of Mathematical Physics, Vol. 9, No. 8, 1968, pp. 1202-1204. doi:10.1063/1.1664700

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.