Soliton—Like Pulses in Vertical Granular Chain Under Gravity：Particle—Like or Wave—Like

We numerically study the propagation, reflection and collision of soliton-like pulses in the vertical granular chain under gravity. For the pure granular chain system, during the propagation and reflection processes at the fixed end, it behaves like a particle. When it is reflected at the free end, it behaves as neither particle-like nor wave-like. When the strengths of the two colliding soliton-like pulses are close, they collide just like particles. When their strengths are greatly different, they collide just like waves. For the soliton behavior in the collision process, from particle-like to wave-like, there is a critical value for the ratio of the strengths of the two initial pulses. For the two-layer granular chain, if the mass of the grains in the second layer is less than that in the first layer, the soliton-like pulse in the first layer usually excites about soliton-like pulses in the second layer.