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Evolution of foliations of the plane is shown, under a condition of constant divergence, to be linked to the scattering problem for the integrable modified Korteweg–de Vries hierarchy. This result is applied to a set of kinematic relations which arise in the theory of ideal fibre-reinforced fluids. In particular, it is established that the fibres, which are convected with the fluid, constitute gen...

On the kinematics of 2+1-dimensional motions of a fibre-reinforced fluid. Integrable connections