Characterization of soliton damping in the granular chain under gravity

A soliton created in the horizontal granular chain damps due to gravity in the vertical chain. We show that there are two types of propagating modes, quasisolitary and oscillatory, in the vertical chain, depending on the strength of impulse. We find that the type of damping is a power law in depth or time. We also find that the absolute value of the exponent of the power law decreases as the strength of the initial impulse increases in the quasisolitary regime. In the oscillatory regime, however, in which the initial impulse is weak, the power-law exponent is independent of the strength of the initial impulse. We show that the power-law damping is caused by the gravitation which results in the change of the force constant at each contact.