for calculation of the LDOS based on the solution of Eilenberger equations for quasiclassical propagator along the trajectories[@Eilenberger]. For numerical treatment of these equations we follow the Refs.  and introduce a Ricatti parametrization for the Green function. The essence of this method is a mathematical trick which allows to solve two first order Ricatti equations instead of fourth-order system of Eilenberger equations. Following Refs.  one can obtain: $$\begin{aligned}
\label{eq:eilenberger}
  \hbar v_F\frac{\partial}{\partial x'}a(x')
  &+[2\tilde{\omega}_n+\Delta^*a(x')]a(x') - \Delta = 0 ,\notag\\
  \hbar v_F\frac{\partial}{\partial x'}b(x') &-
  [2\tilde{\omega}_n + \Delta b(x')]b(x') + \Delta^* = 0,\end{aligned}$$ where $x'=({\bf k}_F{\bf r})/k_F=r\cos(\theta_p-\theta)$ is the coordinate along trajectory, $\Delta({\bf r})=|\Delta|e^{i\Phi}$, $\Phi({\bf r})$ is a superconducting phase, $i\tilde{\omega}_n=i\omega_n+m{\bf v}_F{\bf v}_s$ is a Doppler-shifted Matsubara frequency, $\omega_n=\pi T(2n+1)$ and $${\bf v}_s=\frac{1}{2m}\left(\hbar\nabla\Phi-\frac{2e}{c}{\bf A}\right)$$ is a gauge-invariant superfluid velocity. The LDOS may be expressed through the scalar coherence functions $a$ and $b$ as follows[@Schopohl] $$\begin{aligned}
\label{eq:LDOS}
  N({\bf r},\varepsilon) = \int^{2\pi}_0 \frac{d\theta}{2\pi}
  \text{Re}\left\{\frac{1-ab}{1+ab}\right\}_{i\omega_n \to \varepsilon+i\nu},\end{aligned}$$ where $\varepsilon$ is the quasiparticle energy measured from Fermi level and $\nu$ is a parameter which accounts for an elastic scattering. Throughout this paper we will assume the simplest model[@clem] for the gap function distribution around an isolated vortex positioned at the origin $\Delta({\bf r})=\Delta_0f_1({\bf r})$, where $$\label{Clem-profile}
  f_1({\bf 