  In the field of mathematical physics, there exist many physically interesting
nonlinear dispersive equations with peakon solutions, which are solitary waves
with discontinuous first-order derivative at the wave peak. In this paper, we
apply the multi-layer physics-informed neural networks (PINNs) deep learning to
successfully study the data-driven peakon and periodic peakon solutions of some
well-known nonlinear dispersion equations with initial-boundary value
conditions such as the Camassa-Holm (CH) equation, Degasperis-Procesi equation,
modified CH equation with cubic nonlinearity, Novikov equation with cubic
nonlinearity, mCH-Novikov equation, b-family equation with quartic
nonlinearity, generalized modified CH equation with quintic nonlinearity, and
etc. These results will be useful to further study the peakon solutions and
corresponding experimental design of nonlinear dispersive equations.
