On non-steady planar motions of fibre-reinforced fluids: Geometry and integrable structure

D K Demskoi, W K Schief

Research output: Contribution to journalArticlepeer-review

Abstract

It is shown that the kinematic system describing planar non-steady motions of ideal fibre-reinforced fluids may be reduced to a single two-dimensional third-order partial differential equation in which time enters parametrically. A procedure is established which maps steady motions to non-steady motions. The resulting motions inherit their hidden integrable structure from the steady case. The formalism presented here also readily recovers the connection with the scattering problem of the modified Korteweg–de Vries (mKdV) hierarchy established in previous work.
Original languageEnglish
Article number494001
Pages (from-to)1-12
Number of pages12
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number49
DOIs
Publication statusPublished - 12 Nov 2020

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