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 study generalized Hopf-Cole transformations motivated by the Schr\"odingerbridge problem, which can be seen as a boundary value Hamiltonian system on theWasserstein space. We prove that generalized Hopf-Cole transformations aresymplectic submersions in the Wasserstein symplectic geometry. Many examples,including a Hopf-Cole transformation for the shallow water equations, aregiven. Based on this transformation, energy splitting inequalities areprovided.

Hopf-Cole transformation via generalized Schr\"odinger bridge problem