Comparative analysis of the stability of one-dimensional and spherically symmetric solitons of a scalar field with $J_\mu J^\mu$ self-interaction

Variational method is used for analytical studying of the dynamical stability of solitons. Classes of testfunctions are found which preserve the charge of solitary lumps of the scalar field. Analytical study completed the results of the computer calculations for nonstationary problem shows that in contrast to the one-dimensional case in which the solitons are stable for all $|\omega|<1/\sqrt{2}$, the spherically symmetric solitons are unstable for all $|\omega|<1$ including the region where $H_s<mQ_s$. The eigenvalue problem for finding the growth rates of instability on the linear stage of the latter is formulated.