## Dispersion management for solitons in a Korteweg-de Vries system

preprint

posted on 16.01.2006 by Simon R. Clarke, Boris A. Malomed, Roger Grimshaw#### preprint

Preprints are manuscripts made publicly available before they have been submitted for formal peer review and publication. They might contain new research findings or data. Preprints can be a draft or final version of an author's research but must not have been accepted for publication at the time of submission.

The variable-coefficient Korteweg-de Vries is used to present a basic
model, which has the form of a Korteweg-de Vries equation with a pe-
riodically varying third-order dispersion coefficient, that can take both
positive and negative values. More generally, this model may be extended
to include fifth-order dispersion. Such models describe, for instance, a
periodically modulated waveguide for long gravity-capillary waves. We
develop an analytical approximation for solitary waves in the weakly non-
linear case, from which it is possible to obtain a reduction to a relatively
simple integral equation, which is readily solved numerically. Then, we
describe some systematic direct simulations of the full equation, which
use the soliton shape produced by the integral equation as an initial con-
dition. These simulations reveal regions of stable and unstable pulsating
solitary waves in the corresponding parametric space. Finally, we consider
the effects of fifth-order dispersion.

### History

#### School

- Science

#### Department

- Mathematical Sciences