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

We consider the higher order asymptotics for the modified Korteweg‐de Vries equation in the Painlevé sector. We first show that the solution admits a uniform expansion to all orders in powers of    t   −  1  /  3with coefficients that are smooth functions of    x    (  3  t  )    −  1  /  3. We then consider the special case when the reflection coefficient vanishes at the origin. In this case, the leading coefficient which satisfies the Painlevé II equation vanishes. We show that the leading asymptotics are instead described by the derivative of the Airy function. We are also able to express the subleading term explicitly in terms of the Airy function.

Airy and Painlevé asymptotics for the mKdV equation