Proceedings of the Conference on Nonlinear Coherent Structures in Physics and Biology,
Heriot-Watt University, Edinburgh, July 95

Rational Approximation Methods for Large Amplitude Solitary Waves on Nonlinear Electrical Lattices.

A.C. Hicks ¹, A.K. Common and M.I. Sobhy

¹Electronic Engineering Laboratories,
University of Kent at Canterbury,
Canterbury, Kent, CT2 7NT, U.K.

Abstract

In this paper we describe an approximate method to characterise solitary wave solutions of nonlinear lattice equations. It is based upon one and two point Pade approximations to a series of the real exponential traveling wave solutions of the underlying dispersive system.

The theory is applied to an example of a lattice system which models an experimental nonlinear transmission line and the results obtained are consistent with numerical simulations even for relatively large amplitude solitary waves. The speed--amplitude relation is investigated and compared with that derived using quasi-continuum methods and amplitude versus half--width graphs are also presented. An extended version of most of this work has been submitted to Physica D.

Conference paper.

ABSTRACTS
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