We treat a certain type of degenerate Garnier system such that all the solutions are meromorphic on ℂ2. This is regarded as a two-variable version of the first Painlevé equation. It is shown that, for every solution, each pole locus is expressible by an analytic function which satisfies a fourth-order nonlinear ordinary differential equation. We also give analytic expressions of solutions near their pole loci.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics