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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In his 1892 paper [L. Bianchi, Sulla trasformazione di B\"{a}cklund per lesuperfici pseudosferiche, Rend. Mat. Acc. Lincei, s. 5, v. 1 (1892) 2, 3--12],L. Bianchi noticed, among other things, that quite simple transformations ofthe formulas that describe the B\"{a}cklund transformation of the sine-Gordonequation lead to what is called a nonlocal conservation law in modern language.Using the techniques of differential coverings [I.S. Krasil'shchik, A.M.Vinogradov, Nonlocal trends in the geometry of differential equations:symmetries, conservation laws, and B\"{a}cklund transformations, Acta Appl.Math. v. 15 (1989) 1-2, 161--209], we show that this observation is of a quitegeneral nature. We describe the procedures to construct such conservation lawsand present a number of illustrative examples.

Nonlocal conservation laws of PDEs possessing differential coverings