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

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

2007-01-18

arxiv.org/abs/nlin/0701038v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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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