Study Of The Phase Shift Of Solitary Wave Collision In One-dimensional Granular Chain

Solitary wave is unique in nature which has a single peak.It has been a research topic in physics and fluid mechanics etc.The study of propagation of solitary wave in the granular chain is of great importance in theoretical and practical issues.In this thesis,the phase shift of solitary wave caused by head-on collision in one-dimensional granular chain is studied by theoretical analysis and numerical simulation.Based on the analytical solution of solitary wave for known fully integrable evolution equations,we first compare the theoretical results between Korteweg-de Vries equation and Toda lattice model.The analytical results of phase shift by head-on collision of solitary wave are convinced.Then,the simulation covers the dynamical evolution of collision from the start of incident wave to the end of the collision.The interaction has a central collision region with5-grains width in which two solitary waves have only one peak.Four stages,i.e.,pre-in-phase traveling stage,lag-phase collision state,lead-phase collision state,post-in-phase traveling stage,are introduced to distinguish collision processes.Compared to the propagation of single solitary wave,head-on collision of two solitary waves results in phase lead due to discrete nature of grain.Finally,the conclusion is summarized and the future work is proposed.