Open Access
24 November 2002 Compatible flat metrics
Oleg I. Mokhov
J. Appl. Math. 2(7): 337-370 (24 November 2002). DOI: 10.1155/S1110757X02203149


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).


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Oleg I. Mokhov. "Compatible flat metrics." J. Appl. Math. 2 (7) 337 - 370, 24 November 2002.


Published: 24 November 2002
First available in Project Euclid: 30 March 2003

zbMATH: 1008.37041
MathSciNet: MR1942027
Digital Object Identifier: 10.1155/S1110757X02203149

Primary: 37K10 , 37K15
Secondary: 35Q58 , 37K25 , 53A45 , 53B20 , 53B21 , 53B50

Rights: Copyright © 2002 Hindawi

Vol.2 • No. 7 • 24 November 2002
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