Dynamics of nonlinear waves in a Burridge and Knopoff model for earthquake with long-range interactions, velocity-dependent and hydrodynamics friction forces

•A long-range extension of the Burridge and Knopoff mechanical model of earthquake is investigated.•The model takes into account velocity-dependent and long-range hydrodynamics friction forces.•The complex Ginzburg-Landau equation is obtained through the discrete difference operator technique.•The breather-like soliton solution which represent nonlinear seismic waves propagating in the media is obtained.•The soliton parameters were found to strongly depend of the friction forces. We investigate the dynamics of nonlinear waves in a long-range extension of the Burridge and Knopoff model for earthquake. We consider the dissipative hydrodynamics forces. The spatio-temporal dynamics of the system is found by introducing in the coupling spring and hydrodynamics forces a linear term that decays as a power-law, with an exponent s such that 1