}\exp \left\{ i(\chi (\mp \infty
)-ux/\xi _{S})\right\} ,~  \label{BCInf1}$$$$\Delta _{S}(\mp \infty )=\Delta _{0}\exp \left\{ i(\chi (\mp \infty )-ux/\xi
_{S})\right\} ,  \label{BCINFD}$$$$\Phi _{\infty }=\frac{\Delta _{0}}{1+u^{2}/\sqrt{\Omega ^{2}+|\Phi _{S}|^{2}}},  \label{BCinf2}$$resulting in order parameter phase difference across the structure equal to$$\varphi =\varphi (\infty )-2ux/\xi _{S},~\varphi (\infty )=\chi (\infty
)-\chi (-\infty ).  \label{PhDifInf}$$Here $\varphi (\infty )$ is the asymptotic phase difference across the junction, $\Delta _{0}$ is modulus of order parameters far from the boundaries of the structure at a given temperature, $u=2mv_{s}\xi _{S},$ $m$ is the electron mass and $v_{s}$ is the superfluid velocity. Note that since the boundary conditions (\[BCIF\]) - (\[BCsF\]) include the Matsubara frequency $\Omega $, the phases of $\Phi _{S}$ functions depend on $\Omega $ and are different from the phase of the pair potential $\Delta _{S}$ at the FS interfaces $\chi (d_{F})$ and $\chi (0).$ Therefore it is the value $\varphi (\infty )$ rather than $\varphi =\chi (d_{F})-\chi (0),$ that can be measured experimentally by using a scheme compensating the linear in $x$ part in Eq. (\[PhDifInf\]).

The boundary problem (\[fiS\])-(\[PhDifInf\]) can be solved numerically making use of (\[BCInf1\]), (\[BCinf2\]). Accuracy of calculations can be monitored by equality of currents $J_{S}$ $$\frac{2eJ_{S}(\varphi )}{\pi T\mathcal{A}_{B}}=\sum\limits_{\omega =-\infty
}^{\infty }\frac{iG_{m,\omega }^{2}}{\rho _{m}\widetilde{\Omega 