Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation

WANG Jun-jie, LI Sheng-ping

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

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 2: 172 - 180

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.02.007

Multi-symplectic Geometry and Preissmann Scheme for GSDBM Equation

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

WANG Jun-jie(1981-), male, native of Taiyuan, Shanxi, an associate professor of Pu'er University, engages in multi-symplectic method.

Received date: 2014-09-30

Online published: 2020-10-23

Supported by

Supported by the Differential Equation Innovation Team(CXTD003,2013XYZ19)；

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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

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

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