Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant

Jun Xia, Shuai-Xia Xu, Yu-Qiu Zhao

The Clarkson-McLeod solutions of the fourth Painlevé equation behave like $\kappa D_{\alpha -\frac{1}{2}}^2(\sqrt{2}x)$ as $x\to +\infty$, where $\kappa$ is some real constant and $D_{α-\fr…