Abstract Formulation of the Miura Transform

Yoritaka Iwata
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Yoritaka Iwata: Faculty of Chemistry, Materials and Bioengineering, Kansai University, Osaka 564-8680, Japan

Mathematics, 2020, vol. 8, issue 5, 1-7

Abstract: Miura transform is known as the transformation between Korweg de-Vries equation and modified Korweg de-Vries equation. Its formal similarity to the Cole-Hopf transform has been noticed. This fact sheds light on the logarithmic type transformations as an origin of a certain kind of nonlinearity in the soliton equations. In this article, based on the logarithmic representation of operators in infinite-dimensional Banach spaces, a structure common to both Miura and Cole-Hopf transforms is discussed. In conclusion, the Miura transform is generalized as the transform in abstract Banach spaces, and it is applied to the higher order abstract evolution equations.

Keywords: Miura transform; soliton equations; logarithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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