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, †}

Comparisons between the numerical results on the left-hand side and the analytical one on the right-hand side from Eq. (4) of the evolution of the envelope solitary wave with the different time, where the values of the bead parameters are as follows: Y = 2.03 × 10¹¹ Pa, σ = 0.3, ρ = 7.78 × 10³ kg/m³, R = 0.001 m, δ₀ = 8.46154 × 10⁻⁷ m, ε = 0.005, and k = 0.1.