Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations

P. G. Grinevich

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Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations

P. G. Grinevich

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Abstract

In our paper we construct a new infinite family of symmetries of the Whitham equations (averaged Korteveg-de-Vries equation). In contrast with the ordinary hydrodynamic-type flows these symmetries are nonhomogeneous (i.e. they act nontrivially at the constant solutions), are nonlocal, explicitly depend upon space and time coordinates and form a noncommutative algebra, isomorphic to the algebra of the polynomial vector fields in the complex plane (Virasoro algebra with the zero central charge).

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BibTeX RIS

P. G. Grinevich. 1995-09-13. Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations. https://arxiv.org/abs/solv-int/9509004

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