### Abstract

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrodinger equations. In fibre optics these equations can be used to model single mode fibres under the action of cross-phase modulation, with weak birefringence. The problem is reduced to the '1:2:1' integrable case of the two-particle quartic potential. A general approach for finding elliptic solutions is given. New solutions which are associated with two-gap Treibich-Verdier potentials are found. General quasi-periodic solutions are given in terms of two dimensional theta functions with explicit expressions for frequencies in terms of theta constants. The reduction of quasi-periodic solutions to elliptic functions is discussed.

Original language | English |
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Pages (from-to) | 685-700 |

Number of pages | 16 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 451 |

Issue number | 1943 |

DOIs | |

Publication status | Published - 8 Dec 1995 |

## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*451*(1943), 685-700. https://doi.org/10.1098/rspa.1995.0149