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Bifurcations and highly nonlinear traveling waves in periodic dimer granular chains
Author(s) -
Shen Jianwei,
Miao Baojun,
Luo Jigui
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1453
Subject(s) - traveling wave , mathematics , nonlinear system , phase diagram , diagram , mathematical analysis , phase space , space (punctuation) , phase (matter) , bifurcation diagram , bifurcation , physics , quantum mechanics , computer science , statistics , operating system
In this study, the highly nonlinear waves in periodic dimer granular chains were investigated by the theory of dynamical system and the method of phase diagram analysis. The bifurcations of the different traveling waves in parameter space and those different traveling waves and its phase diagram were given. In addition, the existence of smooth and non‐smooth traveling wave solutions are shown and various sufficient conditions to guarantee the existence of the above solutions were listed. Copyright © 2011 John Wiley & Sons, Ltd.