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Quasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHRÖdinger Equations

P. L. Christiansen·J. C. Eilbeck·V. Z. Enolskii·N. A. Kostov
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Abstract

We consider travelling periodic and quasiperiodic wave solutions of a set of coupled nonlinear Schrödimger equations. In fibre optics these equations can be used to model single mode fibers with strong birefringence and two-mode optical fibres. Recently these equations appear as modes, which describe pulse-pulse interaction in wavelength-division-multiplexed channels of optical fiber transmission systems. Two phase quasi-periodic solutions for integrable Manakov system are given in tems of two-dimensional Kleinian functions. The reduction of quasi-periodic solutions to elliptic functions is dicussed. New solutions in terms of generalized Hermite polynomilas, which are associated with two-gap Treibich-Verdier potentials are found.

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P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, N. A. Kostov. 1999-04-16. Quasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHRÖdinger Equations. https://doi.org/10.1098/rspa.2000.0612

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