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

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

1995-09-13

arxiv.org/abs/solv-int/9509004v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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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