G-Strands and Peakon Collisions on Diff(R)

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Authors: Holm, D.D., Ivanov, R.I.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149231
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: G-Strands and Peakon Collisions on Diff(R) / D.D. Holm, R.I. Ivanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 32 назв. — англ.

A G-strand is a map g: R×R→G for a Lie group G that follows from Hamilton's principle for a certain class of G-invariant Lagrangians. Some G-strands on finite-dimensional groups satisfy 1+1 space-time evolutionary equations that admit soliton solutions as completely integrable Hamiltonian syste...