Solitary waves, periodic peakons and compactons on foliations in a Hertz chain model

For a Hertz chain model, by using the methodology of dynamical systems and singular traveling wave theory developed by Li and Chen [ 9 ] to its traveling wave system defined on a two-dimensional foliations in the three-dimensional space, under different parameter conditions, the existence of all possible bounded solutions (solitary wave solutions, periodic wave solutions, periodic peakons, and compactons) is proved. For the nonlinearity exponent \begin{document}$ k = \frac32, k = 2 $\end{document} and \begin{document}$ k = 3 $\end{document} in the model, as many as 23 exact explicit parametric representations of the above-mentioned traveling wave system are obtained.