The VES experiment has collected high statistics of exclusive reactions with three pions in the final state:
$ \pi^-\pi^-\pi^+ $ (about $43\cdot10^6$ events) and $\pi^-\pi^0\pi^0 $ (about $20\cdot10^6$ events).
The $ 3\pi $ systems are produced by impinging of 28.9 GeV $\pi^-$ beam on the beryllium target.
The dominant production mechanism is the Pomeron exchange between incoming beam pion and the target.
At the very low momentum transfer squared $t'$ the data clearly shows coherent diffractive production
on the whole nucleus which is replaced by incoherent process on the individual nucleons at higher $ 0.05 < t' < 1 $GeV$^2$.
The mass-independent partial wave analysis is performed dividing data into
the bins of $ m(3\pi) $ and $t'$.
The comparison of results with two models of PWA: using formalism of unlimited-rank density matrix
and, using rank=1 is presented.
The predicted isospin relations (assuming $I=1$ of $3\pi$ systems) and observed ones for
intensities in $\pi^-\pi^-\pi^+ $ and $\pi^-\pi^0\pi^0$ are shown.