Title

Conservation Of Phase Space Properties Using Exponential Integrators On The Cubic Schrödinger Equation

Keywords

Exponential integrators; Multisymplectic integrators; Nonlinear Schrödinger equation; Nonlinear spectral diagnostics

Abstract

The cubic nonlinear Schrödinger (NLS) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The "nonlinear" spectrum of the associated Lax pair reveals topological properties of the NLS phase space that are difficult to assess by other means. In this paper we use the invariance of the nonlinear spectrum to examine the long time behavior of exponential and multisymplectic integrators as compared with the most commonly used split step approach. The initial condition used is a perturbation of the unstable plane wave solution, which is difficult to numerically resolve. Our findings indicate that the exponential integrators from the viewpoint of efficiency and speed have an edge over split step, while a lower order multisymplectic is not as accurate and too slow to compete. © 2006 Elsevier Inc. All rights reserved.

Publication Date

7-1-2007

Publication Title

Journal of Computational Physics

Volume

225

Issue

1

Number of Pages

284-299

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jcp.2006.11.030

Socpus ID

34447282836 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/34447282836

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