Soliton-like solutions in nuclear hydrodynamics

It is shown that in the semiclassical limit the equations of nuclear hydrodynamics with Skyrme forces can be reduced to the nonlinear Schroedinger equation ih(partialu/partialt)+(h2/2m)Δu-(3/4)t0Vertical BaruVertical Bar2u -(3/16)t3Vertical BaruVertical Bar4u+lambdau = 0, rho(x, t)equivalentVertical Baru(x, t)Vertical Bar2, phi(x, t)equivalent(h/m)arg u(x,t), which can be used to analyze static and dynamical phenomena in heavy-ion collisions. The main features of the one-dimensional and spherically symmetric soliton solutions are studied and it is shown that they give a good description of the properties of the nuclear density in the ground state. The stability of these solutions is discussed briefly. It is pointed out that spherically symmetric nodal isomeric states of the nuclear density may exist