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 prove that the existence of a dispersionless Lax pair with spectralparameter for a nondegenerate hyperbolic second order partial differentialequation (PDE) is equivalent to the canonical conformal structure defined bythe symbol being Einstein-Weyl on any solution in 3D, and self-dual on anysolution in 4D. The first main ingredient in the proof is a characteristicproperty for dispersionless Lax pairs. The second is the projective behaviourof the Lax pair with respect to the spectral parameter. Both are establishedfor nondegenerate determined systems of PDEs of any order. Thus our main resultapplies more generally to any such PDE system whose characteristic variety is aquadric hypersurface.

Integrability via geometry: dispersionless differential equations in three and four dimensions