NUMERICAL HOMOCLINIC INSTABILITIES IN The SINE-GORDON EQUATION

1 July 1992

journal article
research article
Published by Taylor & Francis in Quaestiones Mathematicae

Vol. 15 (3) , 345-363
https://doi.org/10.1080/16073606.1992.9631696

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.

Keywords

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