Evidence map›Paper›PMID 29887752›Full record

ArticleProceedings. Mathematical, physical, and engineering sciences2018

New variational and multisymplectic formulations of the Euler-Poincaré equation on the Virasoro-Bott group using the inverse map.

Darryl D Holm, Tomasz M Tyranowski

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In one paragraph

Article in Proceedings. Mathematical, physical, and engineering sciences, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.

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2citing papers in PubMed
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1 · What the graph read from it

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3 · Its place in the literature

Who cites it

2 citing papers in PubMed.

  1. Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations.Proceedings. Mathematical, physical, and engineering sciences · 2021
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5 · Who and what money

Authors and funding

2 authors.

Darryl D HolmMathematics Department, Imperial College London, London SW7 2AZ, UK.
Tomasz M TyranowskiMathematics Department, Imperial College London, London SW7 2AZ, UK.ORCID 0000-0002-9078-5950

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler-Poincaré equations defined on the Virasoro-Bott group, by using the inverse map (also called 'back-to-labels' map). This family contains as special cases the well-known Korteweg-de Vries, Camassa-Holm and Hunter-Saxton soliton equations. In the conclusion section, we sketch opportunities for future work that would apply the new Clebsch momentum map with 2-cocycles derived here to investigate a new type of interplay among nonlinearity, dispersion and noise.

Indexed as

Camassa–Holm equationHunter–Saxton equationKorteweg-de Vries equationmultisymplectic partial differential equationsvariational principlesVirasoro–Bott group

Identifiers

PMID29887752
PMCPMC5990699

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