The Discrete Painlevé I Hierarchy

Details The Discrete Painlevé I Hierarchy The Discrete Painlevé I Hierarchy

1997-10-24

arxiv.org/abs/solv-int/9710021v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages in LaTeX. To appear in Proceedings of SIDEII, Kent, UK 1996, (eds) P.A.Clarkson and F.Nijhoff

Scientific paper

The discrete Painlev\'e I equation (dP$\rm_I$) is an integrable difference equation which has the classical first Painlev\'e equation (P$\rm_I$) as a continuum limit. dP$\rm_I$ is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the same linear deformation problem. These form a hierarchy that may be compared to hierarchies of integrable ordinary differential equations (ODEs). We strengthen this comparison by continuum limit calculations that lead to equations in the P$\rm_I$ hierarchy. We propose that our difference equations are discrete versions of higher-order Painlev\'e equations.

Affiliated with

Also associated with

No associations

Rating

The Discrete Painlevé I Hierarchy 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 The Discrete Painlevé I Hierarchy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Discrete Painlevé I Hierarchy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-298464