Equations of Quantum Relativistic Hydrodynamics and Soliton Solutions in Describing Nucleus–Nucleus Collisions

The equations of quantum relativistic hydrodynamics are derived from the Klein–Gordon equation. In the nonrelativistic semiclassical approximation, these equations reduce to the traditional equations of hydrodynamics of a perfect fluid. An analytic solution of hydrodynamic equations in the soliton approximation is found for a collision of nuclear layers in one- and two-dimensional cases. The importance of taking into account nonequilibrium processes is highlighted. The stages of compression, decompression, and expansion are considered by means of a single formula for layers with energies on the order of 10 MeV per nucleon. This reduction of solutions of hydrodynamic equations to soliton solutions was not considered earlier. A generalization to the two-dimensional case leads to the concept of rarefied-bubble formation at the expansion stage. As to the approach itself, it can also be used in other realms of physics in calculations for nonlinear dynamics of vibrations of complex systems.