Parametric Stokes phenomenon for the second Painlevé equation with a large parameter

Details Parametric Stokes phenomenon for the second Painlevé equation with a large parameter Parametric Stokes phenomenon for the second Painlevé equation with a large parameter

2011-06-03

arxiv.org/abs/1106.0612v2

Mathematics

Classical Analysis and ODEs

49 pages, 35 figures

Scientific paper

The second Painlev\'e equation with a large parameter ($P_{II}$) is analyzed by using the exact WKB analysis. The purpose of this study is to investigate the problem of the degeneration of $P$-Stokes geometry of ($P_{II}$), which relates to a kind of Stokes phenomena for asymptotic (formal) solutions of ($P_{II}$). We call this Stokes phenomenon a "parametric Stokes phenomenon". We formulate the connection formula for this Stokes phenomenon, and confirm it in two ways: the first one is by computing the "Voros coefficient" of ($P_{II}$), and the second one is by using the isomonodromic deformation theory. Our main claim is that the connection formulas derived by these two completely different methods coincide.

Affiliated with

Also associated with

No associations

Rating

Parametric Stokes phenomenon for the second Painlevé equation with a large parameter does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Parametric Stokes phenomenon for the second Painlevé equation with a large parameter, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parametric Stokes phenomenon for the second Painlevé equation with a large parameter will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-223638