Classical differential geometry and integrability of systems of hydrodynamic type

Details Classical differential geometry and integrability of systems of hydrodynamic type Classical differential geometry and integrability of systems of hydrodynamic type

1993-03-16

arxiv.org/abs/hep-th/9303092v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages. To be published in: Proc. NATO ARW "Applications of analytic and geometric methods to nonlinear differential equatio

Scientific paper

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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