| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

1. Painlevé Property


    1. Add remark

      Problem 1.1.

      Given an equation with a Painlevé property, how does one identify which linear system it is?


        • Add remark

          Problem 1.2.

          Can one solve the above for discrete Painlevé? (If one has a nonlinear difference equation that one suspects may be Painlevé, can one work out which it is?)


            • Add remark

              Problem 1.3.

              Can one do 1.1 for discrete Painlevé?


                • Add remark

                  Problem 1.4.

                  How does one check the Painlevé property?
                    1. Remark. [Peter Clarkson] Use the Ablowitz-Ramani-Segur algorithm [M.J. Ablowitz, A. Ramani & H. Segur, "A connection between nonlinear evolution equations and ordinary differential equations of P-type. I", J. Math. Phys., 21 (1980), 1006-1015]


                        • Add remark

                          Problem 1.5.

                          In general, is there a classification of determinants that matches that for Painlevé?


                            • Add remark

                              Problem 1.6.

                              Are the spacing distributions of the exceptional groups related to Painlevé?
                                  Answer in Chapter 8 of P. Forrester


                                • Add remark

                                  Problem 1.7.

                                  Is there an integrable structure related to general $\beta$-ensembles?

                                      Cite this as: AimPL: Painleve equations and their applications, available at http://aimpl.org/painleveapp.