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

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

1999-04-16

arxiv.org/abs/solv-int/9904017v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages, no figures

Scientific paper

10.1098/rspa.2000.0612

We consider travelling periodic and quasiperiodic wave solutions of a set of coupled nonlinear Schr\"odimger 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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