  In this paper, we study the following generalized Camassa-Holm equation with
both cubic and quadratic nonlinearities: $$
m_{t}+k_{1}(3uu_{x}m+u^2m_{x})+k_{2}(2mu_{x}+m_{x}u)=0, \quad m=u-u_{xx}, $$
which is presented as a linear combination of the Novikov equation and the
Camassa-Holm equation with constants $k_{1}$ and $k_{2}$. The model is a cubic
generalization of the Camassa-Holm equation. It is shown that the equation
admits single-peaked soliton and periodic peakons.
