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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on January 27, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(1):49-64; doi:10.1093/qjmam/hbl025
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Q. Jl Mech. Appl. Math, Vol. 60. No. 1 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

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

WK Schief{dagger}, C Rogers and S Murugesh

( School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia; Australian Research Council Centre for Mathematics and Statistics of Complex Systems )

{dagger} schief{at}maths.unsw.edu.au


  Abstract

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 generalized tractrices.


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