Slow dynamical behaviors of the propagating signal in granular chain under gravity

A solitary signal created in the horizontal granular chain disperses and damps when it propagates down in the vertical chain because the elastic property of the medium in the vertical chain changes due to gravity. We show that this change in the vertical chain follows power-laws in time, therefore, the type of change is slow dynamical. We derive these power-law behaviors of the signal in the vertical chain when nonlinearity is weak.