Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2, Number 7 (2002), 337-370.
Compatible flat metrics
We solve the problem of description of nonsingular pairs of compatible flat metrics for the general -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).
J. Appl. Math., Volume 2, Number 7 (2002), 337-370.
First available in Project Euclid: 30 March 2003
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 37K15: Integration of completely integrable systems by inverse spectral and scattering methods
Secondary: 37K25: Relations with differential geometry 35Q58 53B20: Local Riemannian geometry 53B21: Methods of Riemannian geometry 53B50: Applications to physics 53A45: Vector and tensor analysis
Mokhov, Oleg I. Compatible flat metrics. J. Appl. Math. 2 (2002), no. 7, 337--370. doi:10.1155/S1110757X02203149. https://projecteuclid.org/euclid.jam/1049074868