  A variation principle is suggested to find self-similar solitary solutions
(``solitons'') of shell model of turbulence. For the Sabra shell model the
shape of the solitons is approximated by rational trial functions with relative
accuracy of O(0.001). It is found how the soliton shape, propagation time $t_n$
and the dynamical exponent $z_0$ (which governs the time rescaling of the
solitons in different shells) depend on parameters of the model. For a finite
interval of $z$ the author discovered ``quasi-solitons'' which approximate with
high accuracy corresponding self-similar equations for an interval of times
from $-\infty$ to some time in the vicinity of the peak maximum or even after
it. The conjecture is that the trajectories in the vicinity of the
quasi-solitons (with continuous spectra of $z$) provide an essential
contribution to the multiscaling statistics of high-order correlation
functions, referred as an ``asymptotic multiscaling''. This contribution may be
even more important than that of the trajectories in the vicinity of the exact
soliton with a fixed value $z_0$. Moreover there are no solitons in some region
of the parameters where quasi-solitons provide dominant contribution to the
asymptotic multiscaling
