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Abstract Formulation of the Miura Transform

Author

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  • Yoritaka Iwata

    (Faculty of Chemistry, Materials and Bioengineering, Kansai University, Osaka 564-8680, Japan)

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.

Suggested Citation

  • Yoritaka Iwata, 2020. "Abstract Formulation of the Miura Transform," Mathematics, MDPI, vol. 8(5), pages 1-7, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:747-:d:355596
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