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

Resurgent-transseries solutions to Painleve equations may be recursivelyconstructed out of these nonlinear differential-equations -- but require Stokesdata to be globally defined over the complex plane. Stokes data explicitlyconstruct connection-formulae which describe the nonlinear Stokes phenomenaassociated to these solutions, via implementation of Stokes transitions actingon the transseries. Nonlinear resurgent Stokes data lack, however, afirst-principle computational approach, hence are hard to determinegenerically. In the Painleve I and Painleve II contexts, nonlinear Stokes dataget further hindered as these equations are resonant, with non-trivialconsequences for the interconnections between transseries sectors, bridgeequations, and associated Stokes coefficients. In parallel to this, thePainleve I and Painleve II equations are string-equations for two-dimensionalquantum (super) gravity and minimal string theories, where Stokes data havenatural ZZ-brane interpretations. This work computes for the first time thecomplete, analytical, resurgent Stokes data for the first two Painleveequations, alongside their quantum gravity or minimal string incarnations. Themethod developed herein, dubbed "closed-form asymptotics", makes sole use ofresurgent large-order asymptotics of transseries solutions -- alongside acareful analysis of the role resonance plays. Given its generality, it may beapplicable to other distinct (nonlinear, resonant) problems. Results foranalytical Stokes coefficients have natural structures, which are described,and extensive high-precision numerical tests corroborate all analyticalpredictions. Connection-formulae are explicitly constructed, with rather simpleand compact final results encoding the full Stokes data, and further allowingfor exact monodromy checks -- hence for an analytical proof of our results.

Resurgent Stokes Data for Painleve Equations and Two-Dimensional Quantum (Super) Gravity