### Abstract

Conservation laws of the nonlinear Schrödinger equation are studied in the presence of higher-order optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive general expressions for infinitely many conserved currents and charges of a coupled higher-order nonlinear Schrödinger equation. The first few currents and associated charges are also presented explicitly. Due to the higher-order effects, the conservation laws of the nonlinear Schrödinger equation are violated in general. The differences between the types of the conserved currents for the Hirota and the Sasa-Satsuma equations imply that the higher-order terms determine the inherent types of conserved quantities for each integrable case of the higher-order nonlinear Schrödinger equation.

Original language | English |
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Pages (from-to) | 6746-6751 |

Number of pages | 6 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 58 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*58*(5), 6746-6751. https://doi.org/10.1103/PhysRevE.58.6746