Abstract Formulation of the Miura Transform
Keyword(s):
De Vries
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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.
1990 ◽
Vol 14
(2)
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pp. 221-224
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1980 ◽
Vol 49
(2)
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pp. 795-801
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1988 ◽
Vol 29
(12)
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pp. 2570-2575
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Keyword(s):
Keyword(s):
Keyword(s):
2005 ◽
Vol 60
(4)
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pp. 221-228
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