Abstract
We study the kinematic equations governing steady motions of an ideal fibre-reinforced fluid in a curved stratum. It turns out that they may be expressed entirely in terms of the intrinsic Gauss equation, which assumes the form of a partial differential equation of third order, for the surface representing the stratum. Integrable cases are isolated by requiring that the Gauss equation be compatible with another third-order hyperbolic differential equation. In particular, a variant of the integrable Tzitzeica equation is derived which encodes orthogonal coordinate systems on pseudospherical surfaces. This third-order equation is related to the Tzitzeica equation by an analogue of the Miura transformation.
| Original language | English |
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| Publication status | Published - 01 Dec 2022 |
| Event | Tenth Workshop on Integrable Systems 2022 - University of Sydney, Sydney, Australia Duration: 01 Dec 2022 → 02 Dec 2022 https://www.maths.usyd.edu.au/u/integrable/2022/programme.html https://www.maths.usyd.edu.au/u/integrable/2022/ (Workshop website) |
Workshop
| Workshop | Tenth Workshop on Integrable Systems 2022 |
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| Country/Territory | Australia |
| City | Sydney |
| Period | 01/12/22 → 02/12/22 |
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