Quasi-stationary nonlinear waves in nuclear matter close to pion condensation

The nuclear hydrodynamic model is extended to include the fluctuating spin-isospin density and its interaction with the nuclear matter density. Using the TDHF equations, it is shown that the dynamics of these densities interacting with the pion field can be expressed in terms of the generalized pressures derivable from the generalized nuclear matter equation of state. A phenomenological Skyrme interaction model is used to obtain these pressures. A theory of pion-like spin-isospin quasi-stationary nonlinear waves is formulated from the generalized hydroequations describing the dynamics of a coupled pion nuclear matter system. In the lowest order of nonlinearity, it is proved that the amplitude of the spin-isospin sound wave satisfies a nonlinear Schrödinger equation. The solution of these equations is the amplitude modulated pion-like solitary waves in nuclear matter. When this matter is near the pion condensate, the speed of these nonlinear waves is much smaller than that of the ordinary sound waves. An implication of the solitary waves excited in such nuclear matter produced in heavy ion collisions is discussed. The characteristic signature of breaking of such waves, produced in a heavy ion central collision, is the emission of a delayed component of correlated nucleons (possibly also with a pion) peaked in the forward direction. It may be that the lighter nuclei³He and³H are produced through such a mechanism.