  The results of the recent experiments on the reaction $\pi^-p\to\pi^0\pi^0n$
performed at KEK, BNL, IHEP, and CERN are analyzed in detail. For the I=0
$\pi\pi$ S wave phase shift $\delta^0_0$ and inelasticity $\eta^0_0$ a new set
of data is obtained. Difficulties emerging when using the physical solutions
for the $\pi^0\pi^0$ S and D wave amplitudes extracted with the partial wave
analyses are discussed. Attention is drawn to the fact that, for the
$\pi^0\pi^0$ invariant mass, m, above 1 GeV, the other solutions, in principle,
are found to be more preferred. For clarifying the situation and further
studying the $f_0(980)$ resonance thorough experimental investigations of the
reaction $\pi^-p\to\pi^0\pi^0n$ in the m region near the $K\bar K$ threshold
are required.
