Classical differential geometry and integrability of systems of hydrodynamic type

1993/03/16 by S. P. Tsarëv, S. P. Tsarev, Tsarev, S. P.
Engineering · Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Elasticity and Wave Propagation #FOS: Mathematics #FOS: Physical sciences #Geotechnical and Geomechanical Engineering #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.hep-th/9303092

12 pages. To be published in: Proc. NATO ARW "Applications of analytic and geometric methods to nonlinear differential equations, 14-19 July 1992, Exeter, UK)

arxiv created 1993/03/16 · openalex publication_date 1993/03/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Remarkable parallelism between the theory of integrable systems of first-order quasilinear PDE and some old results in projective and affine differential geometry of conjugate nets, Laplace equations, their Bianchi-Baecklund transformations is exposed. These results were recently applied by I.M.Krichever and B.A.Dubrovin to prove integrability of some models in topological field theories. Within the geometric framework we derive some new integrable (in a sense to be discussed) generalizations describing N-wave resonant interactions.

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