2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103957In this paper we consider instability of nuclear matter which takes place when the frequencies of the collective excitations turn to zero. We investigate collective excitations with pion quantum numbers J^π=0^-. We study the dependence of zero-frequency solutions of the pion dispersion equation on the value of the spin-isospin quasiparticle interaction G'. The solutions of the pion dispersion equation describe the different types of the excitations in the matter, ω_i(k). At the critical density ρ=ρ_c one of solutions of the definite type turns to zero: ω_{i0}(k_c)=0. When ρ>ρ_c, the excitations ω_{i0}(k) become amplified. It is shown that there is such a "transitional" value of G'=G'_{tr} that for G'<G'_{tr} the zero-frequency solutions belong to the type ω_{sd} while for G'>G'_{tr} they pertain to the type ω_c. The solutions of the type ω_{sd} correspond to instability to small density fluctuations of the nuclear matter at G'\le -1. On the other hand, ω_c is responsible for the "pion condensation" at G'\approx 2. For the stable nuclear matter the branches of solutions ω_{sd}(k) and ω_c(k) are located on the unphysical sheets of the complex plane of frequency.20 pages, 10 figuresNuclear Theorytext