Work

A Local Discontinuous Galerkin method for the modified Camassa--Holm equation

Year: 2026

Type: preprint

Abstract: In this paper, we propose a local discontinuous Galerkin (LDG) method for the modified Camassa-Holm (mCH) equation that contains cubic nonlinearity and high-order derivative terms. Energy conservation and stability are obtained using the conservative and dissipative fluxes, respectively. The error estimate of the semi-discrete scheme is also established. Numerical examples verify that our theoretical findings are sharp and the proposed LDG method is capable of capturing the peakon solution of the mCH equation.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.28077

Authors: Chang, Xiang-Ke, Liu, Yong, Tao, Qi

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, Beijing University of Technology

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Chinese Academy of Sciences, Youth Innovation Promotion Association

Awards: G2856102575, G3027066466, G7236627023, G790494869, G8533620077

OpenAlex ID: W7204807319

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