  The formalism of the coupled $q\bar q$ and the $\varphi\varphi ( \pi-\pi$,
$K\bar K, \pi K,...$) scalar channels is formulated, taking into account the
ground and radial excited $q\bar q$ poles. The basic role is shown to be played
by the transition coefficients $k^{(I)} (q\bar q, |\varphi\varphi)$, which are
calculated using the quark-chiral Lagrangian without free parameters. The
resulting method, called the pole projection mechanism (PPM), ensures: 1) one
resonance for each $\varphi\varphi$ channel from the basic $q\bar q$ pole, e.g.
the $f_0 (500)$ resonance in the $\pi\pi$ channel; 2) a possibility to have two
$\varphi\varphi$ resonances, coupled to the same $q\bar q$ state, when the
channel coupling is taken into account in the meson-meson channels, which
yields $f_0 (500)$ and $f_0(980)$ from the same $n\bar n$ pole around 1 GeV; 3)
the strong pole shift down for special ($\pi\pi, \pi K)$ channels due to large
transition coefficients $k^{(I)}$, computed in this formalism without free
parameters. The parameters of calculated complex poles are in reasonable
agreement with the experimental data of the resonances $f_0(500)$, $f_0(980)$,
$a_0(980)$, $a_0(1450)$, $K^*_0(700)$, $K^*_0(1430)$, $f_0(1370)$ and
$f_0(1710)$.
