dorsal/arxiv
View SchemaQuasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHR\"Odinger Equations
| Authors | P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, N. A. Kostov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9904017 |
| URL | https://arxiv.org/abs/solv-int/9904017 |
| DOI | 10.1098/rspa.2000.0612 |
Abstract
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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"abstract": "We consider travelling periodic and quasiperiodic wave solutions of a set of\ncoupled nonlinear Schr\\\"odimger equations. In fibre optics these equations can\nbe used to model single mode fibers with strong birefringence and two-mode\noptical fibres. Recently these equations appear as modes, which describe\npulse-pulse interaction in wavelength-division-multiplexed channels of optical\nfiber transmission systems. Two phase quasi-periodic solutions for integrable\nManakov system are given in tems of two-dimensional Kleinian functions. The\nreduction of quasi-periodic solutions to elliptic functions is dicussed. New\nsolutions in terms of generalized Hermite polynomilas, which are associated\nwith two-gap Treibich-Verdier potentials are found.",
"arxiv_id": "solv-int/9904017",
"authors": [
"P. L. Christiansen",
"J. C. Eilbeck",
"V. Z. Enolskii",
"N. A. Kostov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1098/rspa.2000.0612",
"title": "Quasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHR\\\"Odinger Equations",
"url": "https://arxiv.org/abs/solv-int/9904017"
},
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