Journal of Applied Mathematics

Journal of Applied Mathematics / 2002 / Article

Open Access

Volume 2 |Article ID 147683 | https://doi.org/10.1155/S1110757X02203149

Oleg I. Mokhov, "Compatible flat metrics", Journal of Applied Mathematics, vol. 2, Article ID 147683, 34 pages, 2002. https://doi.org/10.1155/S1110757X02203149

Compatible flat metrics

Received13 Dec 2001

Abstract

We solve the problem of description of nonsingular pairs of compatible flat metrics for the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated. The integrating of these equations is based on reducing to a special nonlinear differential reduction of the Lamé equations and using the Zakharov method of differential reductions in the dressing method (a version of the inverse scattering method).

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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