  The extended Painlev\'e P.D.E. system $\Delta y -x_1 y - 2 |y|^2y=0$,
$(x_1,\ldots,x_n)\in \mathbb{R}^n$, $y:\mathbb{R}^n\to\mathbb{R}^m$, is
obtained by multiplying by $-x_1$ the linear term of the Ginzburg-Landau
equation $\Delta \eta=|\eta|^2\eta-\eta$,
$\eta:\mathbb{R}^{n}\to\mathbb{R}^{m}$. The two dimensional model $n=m=2$
describes in the theory of light-matter interaction in liquid crystals, the
orientation of the molecules at the boundary of the illuminated region. On the
other hand, the one dimensional model reduces to the second Painlev\'e O.D.E.
$y''-xy-2y^3=0$, $x\in \mathbb{R},$ which has been extensively studied, due to
its importance for applications. The solutions of the extended Painlev\'e
P.D.E. share some characteristics both with the Ginzburg-Landau equation and
the second Painlev\'e O.D.E. The scope of this paper is to construct standard
vortex solutions $y:\mathbb{R}^{n}\to\mathbb{R}^{n-1}$ ($\forall n\geq 3$) of
the extended Painlev\'e equation. These solutions have in every hyperplane
$x_1=\mathrm{Const.}$, a profile similar to the standard vortices
$\eta:\mathbb{R}^{n-1}\to\mathbb{R}^{n-1}$ of the Ginzburg-Landau equation, but
their amplitude is determined by the Hastings-McLeod solution $h$ of the second
Painlev\'e O.D.E. evaluated at $x_1$.
