Original Articles

NUMERICAL HOMOCLINIC INSTABILITIES IN The SINE-GORDON EQUATION

Published in: Quaestiones Mathematicae
Volume 15 , issue 3 , 1992 , pages: 345–363

DOI: 10.1080/16073606.1992.9631696

Author(s): B.M. Herbst Department of Applied Mathematics, South Africa , M.J. Ablowitz Program in Applied Mathematics,

Keywords: 65L07 , 58F05 , 58F07

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Abstract

Solutions of the sine-Gordon equation obtained from some of the usual numerical methods, can display irregular behavior if the initial conditions are specified in the vicinity of a homoclinic orbit. We concentrate on the instabilities caused by the time discretization and show that the use of symplectic methods may avoid the instabilities.

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