Heriot-Watt Mathematics Report Series
HWM00-11, 22 May 2000
Quasi-periodic and periodic solutions for vector nonlinear Schrödinger equations
JC Eilbeck, VZ Enolskii and NA Kostov
Abstract
We consider quasi-periodic and periodic (cnoidal) wave solutions of a set of
$n$-component vector nonlinear Schr{ö}dinger equations
(VNLSE). In a biased photorefractive crystal with a drift mechanism
of nonlinear response and Kerr-type nonlinearity, $n$ component
nonlinear Schrödinger equations can be used to model
self-trapped mutually incoherent wave packets. These
equations also model pulse-pulse interactions in
wavelength-division-multiplexed channels of optical fibre
transmission systems. Quasi-periodic wave solutions for the VNLSE in
terms of $n$-dimensional Kleinian functions are presented. Periodic
solutions in terms of Hermite polynomials and generalized Hermite
polynomials for $n$-component nonlinear Schrödinger equations are
found.
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Publication
J C Eilbeck, V Z Enol'skii, N A Kostov
, Quasi-periodic and periodic solutions for vector nonlinear Schrodinger equations, J Math Phys, 41, 8236-8248, (2000).
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