School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
7-18-2024
Abstract
In this paper, the multi-symplectic formulations of the two-component Camassa–Holm system are presented. Both the multi-symplectic structure and two local conservation laws of the generalized two-component Camassa–Holm model are proposed for its first-order canonical form. Then, combining the Fourier pseudo-spectral method in the spatial domain with the midpoint method in the time dimension, the multi-symplectic Fourier pseudo-spectral scheme is constructed for the first-order canonical form. Meanwhile, the discrete scheme of the residuals of the multi-symplectic structure and two local conservation laws are also provided. By using the multi-symplectic Fourier pseudo-spectral scheme, the evolution of one- and two-soliton solutions for the generalized two-component Camassa–Holm model is regained. The structure-preserving properties and the reliability of the numerical scheme are illustrated by the tiny numerical residuals (less than 3.5 × 10−8) of the conservation laws as well as the tiny numerical variations (less than 1 × 10−9) of the amplitudes and the propagating velocities of the solitons.
Recommended Citation
Xi, Xiaojian, Weipeng Hu, Bo Tang, Pingwei Deng, and Zhijun Qiao. "Multi-Symplectic Method for the Two-Component Camassa–Holm (2CH) System." Journal of Nonlinear Mathematical Physics 31, no. 1 (2024): 1-15. https://doi.org/10.1007/s44198-024-00216-x
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Journal of Nonlinear Mathematical Physics
DOI
https://doi.org/10.1007/s44198-024-00216-x
Comments
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