On the bicycle transformation and the filament equation: results and conjectures

DOI10.1016/j.geomphys.2016.05.013zbMath1375.37159arXiv1602.06455OpenAlexW2286946833WikidataQ123231373 ScholiaQ123231373MaRDI QIDQ2400271

Sergei Tabachnikov

Publication date: 28 August 2017

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.06455

zbMATH Keywords

monodromycomplete integrabilityfilament equationBäcklund transformationbicycle correspondence

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Kinematics of mechanisms and robots (70B15) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Differential geometric aspects in kinematics (53A17)

Related Items (7)

Infinitesimal Darboux transformation and semi-discrete MKDV equation ⋮ Self-Bäcklund curves in centroaffine geometry and Lamé’s equation ⋮ Bicycling geodesics are Kirchhoff rods ⋮ Periodic discrete Darboux transforms ⋮ Book review of: R. D. Mauldin, The Scottish Book. Mathematics from the Scottish Café. With selected problems from the New Scottish Book. 2nd ed. ⋮ On centro-affine curves and Bäcklund transformations of the KdV equation ⋮ Zindler-type hypersurfaces in \(\mathbb{R}^4\)

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