Wave-Breaking Phenomena in Quark-Gluon Plasma

We investigate the onset of wave-breaking in the quark-gluon plasma (QGP) formed in heavy-ion collisions at both RHIC and the LHC. A nonlinear longitudinal color field is coupled to a three-dimensional viscous hydrodynamic background constrained by experimental conditions: Pb-Pb at $\sqrt{s_{\rm NN}}=5.02$ TeV (LHC) and Au-Au at $\sqrt{s_{\rm NN}}=200$ GeV (RHIC). The instantaneous wave-breaking threshold is determined from the in-medium plasma frequency, while the field evolution follows a nonlinear Landau equation with Debye screening and expansion damping. At the LHC, the higher initial temperature and density drive the system above the threshold within $\tau \lesssim$ 2.3 fm/$c$, whereas at RHIC the cooler and more dilute medium delays wave-breaking to $\tau \simeq 2.8$~fm/$c$. Scans over initial temperature, density, thermalization time, QGP lifetime, and collision system (RHIC vs LHC) confirm the robustness of this instability against parameter variations. These results identify wave-breaking as a universal microscopic mechanism for the early loss of coherence and rapid onset of hydrodynamics in the QGP, providing a common explanation for the fast equilibration observed at both RHIC and the LHC.