@Article{CiCP-19-1,
author = {},
title = {Geometric Numerical Integration for Peakon b-Family Equations},
journal = {Communications in Computational Physics},
year = {2016},
volume = {19},
number = {1},
pages = {24--52},
abstract = {<p style="text-align: justify;">In this paper, we study the Camassa-Holm equation and the Degasperis-Procesi
equation. The two equations are in the family of integrable peakon equations,
and both have very rich geometric properties. Based on these geometric structures, we
construct the geometric numerical integrators for simulating their soliton solutions.
The Camassa-Holm equation and the Degasperis-Procesi equation have many common
properties, however, they also have the significant differences, for example, there
exist the shock wave solutions for the Degasperis-Procesi equation. By using the symplectic
Fourier pseudo-spectral integrator, we simulate the peakon solutions of the two
equations. To illustrate the smooth solitons and shock wave solutions of the DP equation,
we use the splitting technique and combine the composition methods. In the
numerical experiments, comparisons of these two kinds of methods are presented in
terms of accuracy, computational cost and invariants preservation.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.171114.140715a},
url = {https://global-sci.com/article/80244/geometric-numerical-integration-for-peakon-b-family-equations}
}