Envelope solitary waves and their reflection and transmission due to impurities in a granular material<xref rid="cpb_27_1_014501fn1" ref-type="fn">*</xref> <fn id="cpb_27_1_014501fn1"> <label>*</label> <p>Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA01020304) and the National Natural Science Foundation of China (Grant Nos. 91026005, 11547304, 11275156, 11047010, and 61162017).</p> </fn>

Envelope solitary waves and their reflection and transmission due to impurities in a granular material* *

Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA01020304) and the National Natural Science Foundation of China (Grant Nos. 91026005, 11547304, 11275156, 11047010, and 61162017).

Du Wen-Qing¹, Sun Jian-An¹, Yang Yang-Yang², Duan Wen-Shan^{1, †}

(color online) (a) Dependences of the kinetic energy ratios of both transmitted wave and reflected wave on the number of the impurity materials. Dependences of the period and the length of the vibration of the kinetic energy ratios on the wavenumber k and the parameter α and ΔL = x₂ − x₁.