This article is cited in 5 papers

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

D. V. Zakharov

Columbia University

Abstract: We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. On the moduli space of algebraic Riemann surfaces, we construct flows that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.

Keywords: isoperiodic deformation, periodic acoustic operator, finite-gap solution, integrable system.

Received: 27.12.2006

DOI: 10.4213/tmf6120

 English version: Theoretical and Mathematical Physics, 2007, 153:1, 1388–1397

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