Asymptotic forms of solutions to the fourth Painlevé equation

Abstract

We consider the fourth Painleve equation with nonzero values of its two complex parameters a and b . Asymptotic forms of power, complicated, exotic, and elliptic types for its solutions near the points x = 0 and x = ∞ are sought by methods of two- and three-dimensional power geometry. We obtain nine families of power asymptotic forms extended by asymptotic expansions and one family of elliptic asymptotic forms. Complicated and exotic asymptotic forms are absent.