On the properties of solutions of equations in the \(K_{2}\) hierarchy
The author studies the properties of solutions of equations in the \(K_2\) hierarchy. The focus of the paper is on the sixth order equation in this hierarchy. Conditions for the existence of families of solutions with movable poles are obtained. The polynomial Hamiltonian is given. The Bäcklund transformations are derived. Meromorphic solutions are represented as ratios of special entire functions and the criteria for the existence of rational solutions are presented.
Painleve equations and higher order generalizations
scientific article; zbMATH DE number 5659338