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

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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15 pages

Scientific paper

10.1007/s11232-007-0122-0

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

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