GSDBM方程的多辛几何和多辛Preissman格式研究

doi:10.13371/j.cnki.chin.q.j.m.2017.02.007

数学季刊 ›› 2017, Vol. 32 ›› Issue (2): 172-180.doi: 10.13371/j.cnki.chin.q.j.m.2017.02.007

GSDBM方程的多辛几何和多辛Preissman格式研究

1. Department of Mathematics, Pu'er University2. Department of Mathematics,Northwest University

收稿日期:2014-09-30 出版日期:2017-06-30 发布日期:2020-10-23
作者简介:WANG Jun-jie(1981-), male, native of Taiyuan, Shanxi, an associate professor of Pu'er University, engages in multi-symplectic method.
基金资助:
Supported by the Differential Equation Innovation Team(CXTD003,2013XYZ19)；

Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation

1. Department of Mathematics, Pu'er University2. Department of Mathematics,Northwest University

Received:2014-09-30 Online:2017-06-30 Published:2020-10-23
About author:WANG Jun-jie(1981-), male, native of Taiyuan, Shanxi, an associate professor of Pu'er University, engages in multi-symplectic method.
Supported by:
Supported by the Differential Equation Innovation Team(CXTD003,2013XYZ19)；

摘要/Abstract

摘要： The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.

关键词: Dodd-Bullough-Mikhailov equation, multi-symplectic theory, Hamilton space, Preissmann scheme, local conservation laws

Abstract: The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.

Key words: Dodd-Bullough-Mikhailov equation, multi-symplectic theory, Hamilton space; Preissmann scheme, local conservation laws

中图分类号:

O241.8

王俊杰, 李胜平.

GSDBM方程的多辛几何和多辛Preissman格式研究

[J]. 数学季刊, 2017, 32(2): 172-180.

WANG Jun-jie, LI Sheng-ping. Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(2): 172-180.

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GSDBM方程的多辛几何和多辛Preissman格式研究

Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation

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