Multi-Symplectic Method for the Two-Component Camassa–Holm (2CH) System

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
Xiaojian Xi, Weipeng Hu, Bo Tang, Pingwei Deng, Zhijun Qiao
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引用次数: 0

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.

Abstract Image

双分量卡马萨-霍尔姆(2CH)系统的多交映法
本文提出了双分量卡马萨-霍姆系统的多交映公式。针对广义双分量 Camassa-Holm 模型的一阶典型形式,提出了该模型的多交映结构和两个局部守恒定律。然后,结合空间域的傅立叶伪谱法和时间维的中点法,构建了一阶典型形式的多交映傅立叶伪谱方案。同时,还提供了多交映结构残差的离散方案和两个局部守恒定律。通过使用多折射傅立叶伪谱方案,重新获得了广义双分量卡马萨-霍姆模型的单孑子和双孑子解的演化。守恒定律的微小数值残差(小于 3.5 × 10-8)以及孤子振幅和传播速度的微小数值变化(小于 1 × 10-9)说明了数值方案的结构保持特性和可靠性。
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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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