SYMPLECTIC METHODS FOR THE NONLINEAR SCHRODINGER-EQUATION

Authors
HERBST BM VARADI F ABLOWITZ MJ
Citation
Bm. Herbst et al., SYMPLECTIC METHODS FOR THE NONLINEAR SCHRODINGER-EQUATION, Mathematics and computers in simulation, 37(4-5), 1994, pp. 353-369
Citations number
22
Categorie Soggetti
Computer Sciences",Mathematics,"Computer Science Interdisciplinary Applications","Computer Science Software Graphycs Programming
Journal title
Mathematics and computers in simulation → ACNP
ISSN journal
03784754
Volume
37
Issue
4-5
Year of publication
1994
Pages
353 - 369
Database
ISI
SICI code
0378-4754(1994)37:4-5<353:SMFTNS>2.0.ZU;2-#
Abstract
Various symplectic discretizations of the nonlinear Schrodinger equati on are compared, including one for the integrable discretization due t o Ablowitz and Ladik. The numerical experiments are performed with ini tial values taken near a homoclinic orbit, i.e., in a situation where integrability is crucial. It is shown that symplectic discretizations can sometimes lead to remarkable improvements, and that in even more s ensitive situations some of our best numerical schemes fail.