Homoclinic manifolds and numerical chaos in the nonlinear Schrödinger equation

Mark J. Ablowitz and Constance M. Schober

Mathematics and Computers in Simulation (MATCOM), 1994, vol. 37, issue 4, 249-264

Abstract: Crossings of homoclinic manifolds is a well known mechanism underlying observed chaos in low dimensional systems. We discuss an analogous situation as it pertains to the numerical simulation of a well known integrable partial differential equation, the nonlinear Schrödinger equation. In various parameter regimes, depending on the initial data, numerical chaos is observed due to either truncation effects or errors on the order of roundoff. The explanation of the underlying cause of the chaos being due to crossing of homoclinic manifolds induced by the numerical errors is elucidated. The nonlinear Schrödinger equation is prototypical of a much wider class of nonlinear systems in which computational chaos can be a significant factor.

Date: 1994
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378475494000182
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:37:y:1994:i:4:p:249-264

DOI: 10.1016/0378-4754(94)00018-2

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().