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The resonant nonlinear Schrödinger equation in cold plasma physics. Application of Bäcklund–Darboux transformations and superposition principles

Published online by Cambridge University Press:  01 April 2007

J.-H. LEE ,
O.K PASHAEV ,
C. ROGERS  and
W.K. SCHIEF
J.-H. LEE
Affiliation:
Institute of Mathematics, Academia Sinica, Taiwan ([email protected])
O.K PASHAEV
Affiliation:
Department of Mathematics, Izmir Institute of Technology, Turkey ([email protected])
C. ROGERS
Affiliation:
School of Mathematics, University of New South Wales, Sydney, Australia ([email protected]) Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems ([email protected])
W.K. SCHIEF
Affiliation:
School of Mathematics, University of New South Wales, Sydney, Australia ([email protected]) Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems ([email protected])
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Abstract.

A system of nonlinear equations governing the transmission of uni-axial waves in a cold collisionless plasma subject to a transverse magnetic field is reduced to the recently proposed resonant nonlinear Schrödinger (RNLS) equation. This integrable variant of the standard nonlinear Schrödinger equation admits novel nonlinear superposition principles associated with Bäcklund–Darboux transformations. These are used here, in particular, to construct analytic descriptions of the interaction of solitonic magnetoacoustic waves propagating through the plasma.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 2 , April 2007 , pp. 257 - 272
Copyright
Copyright © Cambridge University Press 2006

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