arXiv subjects

O. I. Mokhov

Publications and source records attributed to O. I. Mokhov.

21 records · Page 2Linked to original sources

arXiv2002

Compatible flat metrics

We solve the problem of description for nonsingular pairs of compatible flat metrics in 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 Lame equations and using the Zakharov method of differential reductions in the dressing method (a version of the inverse scattering method).

math.DG↗

arXiv2000

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

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).

math.DG↗

arXiv2000

Compatible and Almost Compatible Pseudo-Riemannian Metrics

Notions of compatible and almost compatible pseudo-Riemannian metrics, which are motivated by the theory of compatible (local and nonlocal) Poisson structures of hydrodynamic type and generalize the notion of flat pencil of metrics, are introduced and studied.

math.DG↗