On the preservation of phase space structure under multisymplectic discretization

    Authors

    A. L. Islas;C. M. Schober

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    J. Comput. Phys.

    Keywords

    multisymplectic integrators; nonlinear spectral diagnostics; nonlinear; schrodinger equation; Sine-Gordon equation; SYMPLECTIC INTEGRATORS; HAMILTONIAN PDES; EQUATIONS; BEHAVIOR; WAVES; Computer Science, Interdisciplinary Applications; Physics, Mathematical

    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 Schrodinger 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. (C) 2004 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Computational Physics

    Volume

    197

    Issue/Number

    2

    Publication Date

    1-1-2004

    Document Type

    Article

    Language

    English

    First Page

    585

    Last Page

    609

    WOS Identifier

    WOS:000222184700009

    ISSN

    0021-9991

    Share

    COinS