English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We investigate geometric evolution equations for Legendrian curves in the3-sphere which are invariant under the action of the unitary group U(2). Wedefine a natural symplectic structure on the space of Legendrian loops, andshow that the modified Korteweg-deVries equation, along with its associatedhierarchy, are realized as curvature evolutions induced by a sequence ofHamiltonian flows. For the flow among these that induces the mKdV equation, weinvestigate the geometry of solutions which evolve by rigid motions in U(2).Generalizations of our results to higher-order evolutions and curves in similargeometries are also discussed.

mKdV-Related Flows for Legendrian Curves in the Pseudohermitian 3-Sphere