On the preservation of phase space structure under multisymplectic discretization
Abbreviated Journal Title
J. Comput. Phys.
multisymplectic integrators; nonlinear spectral diagnostics; nonlinear; schrodinger equation; Sine-Gordon equation; SYMPLECTIC INTEGRATORS; HAMILTONIAN PDES; EQUATIONS; BEHAVIOR; WAVES; Computer Science, Interdisciplinary Applications; Physics, Mathematical
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 of Computational Physics
"On the preservation of phase space structure under multisymplectic discretization" (2004). Faculty Bibliography 2000s. 4453.