Pure imaginary solutions of the second Painlevé equation
The paper deals with the second Painlevé equation of the form \[ y''= 2y^3+ 2y+ i\alpha,\quad \alpha\in\mathbb{R}. \] The author proves the existence of pure imaginary solutions and their asymptotics as \(x\to\infty\) which are infinitely differentiable. Some specific cases of the equation are considered in detail.
scientific article; zbMATH DE number 2171759