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Hydrodynamic reductions of the dispersionless Harry Dym hierarchy

Jen-Hsu Chang

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We investigate the reductions of the dispersionless Harry Dym hierarchy to systems of finitely many partial differential equations. These equations must satisfy the compatibility condition and they are diagonalizable and semi-Hamiltonian. By imposing a further constraint, the compatibility is reduced to a system of algebraic equations, whose solutions are described.


PACS

02.30.Ik Integrable systems

02.30.Jr Partial differential equations

MSC

37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

35N10 Overdetermined systems with variable coefficients (general)

Subjects

Mathematical physics

Dates

Issue 29 (22 July 2005)

Received 12 March 2005

Published 6 July 2005



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