### Abstract

We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form φ_{n+1} + φ_{n-1} = F(φ_{n}). Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case.

Original language | English |
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Pages (from-to) | 214-220 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 311 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 2003 May 12 |

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### Keywords

- Discrete solitons
- Hirota method
- Singularity confinement

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*311*(2-3), 214-220. https://doi.org/10.1016/S0375-9601(03)00499-7