论文标题
Miura转换的抽象表述
Abstract formulation of the Miura transform
论文作者
论文摘要
Miura变换被称为Korteweg De-Vries方程与修改的Korteweg De-Vries方程之间的变换。它与Cole-Hopf转换的正式相似性已被注意到。这个事实将对数类型转换视为孤子方程中某些非线性的起源。在本文中，讨论了Miura和Cole-Hopf变换的共同结构，基于无限二维Banach空间中操作员的对数表示。总之，Miura转换被推广为抽象Banach空间中的变换，并应用于高阶抽象演化方程。
Miura transform is known as the transformation between Korteweg de-Vries equation and modified Korteweg 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 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.
