@Article{CiCP-19-4,
author = {},
title = {On Invariant-Preserving Finite Difference Schemes for the Camassa-Holm Equation and the Two-Component Camassa-Holm System},
journal = {Communications in Computational Physics},
year = {2016},
volume = {19},
number = {4},
pages = {1015--1041},
abstract = {<p style="text-align: justify;">The purpose of this paper is to develop and test novel invariant-preserving
finite difference schemes for both the Camassa-Holm (CH) equation and one of its
2-component generalizations (2CH). The considered PDEs are strongly nonlinear, admitting
soliton-like peakon solutions which are characterized by a slope discontinuity
at the peak in the wave shape, and therefore suitable for modeling both short wave
breaking and long wave propagation phenomena. The proposed numerical schemes
are shown to preserve two invariants, momentum and energy, hence numerically producing
wave solutions with smaller phase error over a long time period than those
generated by other conventional methods. We first apply the scheme to the CH equation
and showcase the merits of considering such a scheme under a wide class of initial
data. We then generalize this scheme to the 2CH equation and test this scheme under
several types of initial data.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.130115.110915a},
url = {https://global-sci.com/article/80283/on-invariant-preserving-finite-difference-schemes-for-the-camassa-holm-equation-and-the-two-component-camassa-holm-system}
}