Soliton-like excitations in a one-dimensional nuclear matter

Are considered the nonlinear Schroedinger equation with phi3-phi5 nonlinearity describing static and dynamic properties of heavy ions. Saturating soliton-like solution which can be interpreted as a kernel is explicitly found under the zero boundary conditions. It is demonstrated that the said equation may be used not only to describe the motion of a nucleus as a whole, but also to investigate internal excitations in a nuclear matter. Only hole-like, but no way hump-like stable localized solitons can travel in the nuclear matter. Those solitons when propagating near the velocity of sound are shown to be approximately described by the Korteweg-de Vries equation. Also are given exact expressions for them and for some other localized solutions. Stability analysis of the found soliton-like configurations is presented