On Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics

Details On Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics On Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics

2000-05-09

arxiv.org/abs/math/0005081v1

Mathematics

Differential Geometry

15 pages

Scientific paper

We deal with the problem of description of nonsingular pairs of compatible flat metrics for the general $N$-component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics). It is based on the reducing this problem to a special reduction of the Lame equations and the using the Zakharov method of differential reductions in the dressing method (a version of the inverse scattering method).

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