Rational solutions of difference Painlevé equations
The author captures all rational solutions of some difference Painlevé equations of PI and PII types. For non-autonomous cases it is shown that all rational solutions of the difference PII equations are generated by successive applications of auto-Bäcklund transformations to the seed solution vanishing identically, and that other equations of PI type admit no rational solutions. For autonomous cases all nontrivial rational solutions are obtained, and they exist under a certain condition on a fixed point of the equation. If such a condition is not satisfied, there exist solutions that are rational in an exponential function.
scientific article; zbMATH DE number 6073763
scientific article