Title

On The Preservation Of Phase Space Structure Under Multisymplectic Discretization

Keywords

Multisymplectic integrators; Nonlinear Schrödinger equation; Nonlinear spectral diagnostics; Sine-Gordon equation

Abstract

In this paper we explore the local and global properties of multisymplectic discretizations based on finite differences and Fourier spectral approximations. Multisymplectic (MS) schemes are developed for two benchmark nonlinear wave equations, the sine-Gordon and nonlinear Schrödinger equations. We examine the implications of preserving the MS structure under discretization on the numerical scheme's ability to preserve phase space structure, as measured by the nonlinear spectrum of the governing equation. We find that the benefits of multisymplectic integrators include improved resolution of the local conservation laws, dynamical invariants and complicated phase space structures. © 2004 Elsevier Inc. All rights reserved.

Publication Date

7-1-2004

Publication Title

Journal of Computational Physics

Volume

197

Issue

2

Number of Pages

585-609

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jcp.2003.12.010

Socpus ID

3242702916 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/3242702916

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