Nonisospectral Symmetries of the KdV Equation and the Corresponding Symmetries of the Whitham Equations

  • P. G. Grinevich
Part of the NATO ASI Series book series (NSSB, volume 320)


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 plain.


Modulus Space Riemann Surface Branch Point Marked Point Riemann Problem 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • P. G. Grinevich
    • 1
  1. 1.L.D.Landau Institute for Theoretical PhysicsMoscowUSSR

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