Analytical Solutions and Collision Stability Analysis of Solitary Waves in a Pre-compressed One-dimensional Granular Crystal

In this paper, the governing equation in a pre-compressed one-dimensional granular crystal, which was previously discussed by Nesterenko [J. Appl. Mech. Phys. 24, 733 (1983)], is solved analytically. Multiple solitary wave solutions are obtained by using the homogeneous balance principle and Hirota’s bilinear method. We analyze the difference between the original system and the KdV system and examine the collision of solitary waves in some special parameters. The dynamic behavior and stability of the double solitary waves are also studied. We find that the opposite collision between single solitary waves may be stable and thus generate a stable double solitary wave. It is concluded that the collision is a special stable double solitary wave solution. We further propose a possible way to determine the stability of multiple solitary waves qualitatively.