Compatible flat metrics

Compatible flat metrics

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 foun...

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Main Author: Oleg I. Mokhov
Format: Article
Language:English
Published: Hindawi Limited 2002-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/S1110757X02203149
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spelling doaj-59be864d83124b57ad507e6a8217ac3e2020-11-24T23:21:01ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422002-01-012733737010.1155/S1110757X02203149Compatible flat metricsOleg I. Mokhov0Centre for Nonlinear Studies, L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 2 Kosygina Street, Moscow 117940, RussiaWe 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).http://dx.doi.org/10.1155/S1110757X02203149
collection DOAJ
language English
format Article
sources DOAJ
author Oleg I. Mokhov
spellingShingle Oleg I. Mokhov
Compatible flat metrics
Journal of Applied Mathematics
author_facet Oleg I. Mokhov
author_sort Oleg I. Mokhov
title Compatible flat metrics
title_short Compatible flat metrics
title_full Compatible flat metrics
title_fullStr Compatible flat metrics
title_full_unstemmed Compatible flat metrics
title_sort compatible flat metrics
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2002-01-01
description 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).
url http://dx.doi.org/10.1155/S1110757X02203149
work_keys_str_mv AT olegimokhov compatibleflatmetrics
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