  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 the non-extensive equation of state. We have
shown that the equations, describing the propagation of nonlinear waves under
such situation are KdV-type (Korteweg-De Vries). 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.
