Quasi-periodic and periodic solutions for coupled nonlinear Schrödinger equations of Manakov type
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.
- Publication:
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Proceedings of the Royal Society of London Series A
- Pub Date:
- September 2000
- DOI:
- 10.1098/rspa.2000.0612
- arXiv:
- arXiv:solv-int/9904017
- Bibcode:
- 2000RSPSA.456.2263C
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 21 pages, no figures