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Padé approximants and nonlinear waves

Published online by Cambridge University Press:  13 March 2009

F. J. Romerias  and
J. P. Dougherty
F. J. Romerias
Affiliation:
Centro do Electrodinâmica, Instituto Superior Técnico, Lisboa-1, Portugal
J. P. Dougherty
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, U.K.
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Abstract

The perturbation solution of the ordinary differential equations that describe exact nonlinear travelling plane waves leads to asymptotic expansions in powers of the (small) wave amplitude for both the proffle and the frequency of the waves. This paper shows how the Padé approximant method can be used to extend the validity of those expansions to larger amplitudes. The method is applied to the Duffing equation and to two types of nonlinear waves in a cold electron plasma: longitudinal oscillations and coupled transverse–longitudinal relativistic waves.

Type
Research Article
Information
Journal of Plasma Physics , Volume 21 , Issue 3 , June 1979 , pp. 549 - 571
Copyright
Copyright © Cambridge University Press 1979

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