TY - JOUR

T1 - Quasi-periodic and periodic solutions for systems of coupled nonlinear Schrodinger equations of Manakov type

AU - Christiansen, P. L.

AU - Eilbeck, John Christopher

AU - Enol'skii, V. Z.

AU - Kostov, N. A.

PY - 2000

Y1 - 2000

N2 - We consider travelling periodic and quasi–periodic wave solutions in coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single–mode fibres with strong birefringence, and two–mode optical fibres. Recently these equations appear as a model describing pulse–pulse interactions in wavelength–division–multiplexed channels of optical fibre transmission systems. In some cases this model reduces to the integrable Manakov system (IMS). Two–phase quasi–periodic solutions for the IMS are given in terms of two–dimensional Kleinian functions. The reduction of quasi–periodic solutions to elliptic functions is discussed. New solutions are found in terms of generalized Hermite polynomials, which are associated with two–gap Treibich–Verdier potentials.

AB - We consider travelling periodic and quasi–periodic wave solutions in coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single–mode fibres with strong birefringence, and two–mode optical fibres. Recently these equations appear as a model describing pulse–pulse interactions in wavelength–division–multiplexed channels of optical fibre transmission systems. In some cases this model reduces to the integrable Manakov system (IMS). Two–phase quasi–periodic solutions for the IMS are given in terms of two–dimensional Kleinian functions. The reduction of quasi–periodic solutions to elliptic functions is discussed. New solutions are found in terms of generalized Hermite polynomials, which are associated with two–gap Treibich–Verdier potentials.

U2 - 10.1098/rspa.2000.0612

DO - 10.1098/rspa.2000.0612

M3 - Article

SN - 0080-4630

VL - 456

SP - 2263

EP - 2281

JO - Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences

JF - Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences

IS - 2001

ER -