Nonlinear waves in a hot, viscous and non-extensive quark-gluon plasma

The effects of the non-extensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics with non-extensive equation of state. We have shown that the equations, describing the propagation of nonlinear waves under such situation admit solutions similar to that of KdV-type (Korteweg-De Vries) equations. Apart from their preserved solitonic behaviour the dissipative nature of these waves are also observed. The waves with larger amplitude and width dissipate less and propagate faster and these waves deplete more for both smaller values of Tsallis parameter (q) and temperature (T) of the medium. For vanishingly small transport coefficients the nonlinear waves show breaking nature. These findings suggest that the nature of the propagation of the nonlinear waves may serve as a good probe to differentiate between the extensive and non-extensive thermodynamic nature of a fluid, such as the quark-gluon plasma, produced in relativistic nuclear collisions.