### Abstract

Using a direct ansatz approach, we have found a number of periodic zero-velocity analytic solutions of the complex quintic Swift-Hohenberg equation (CSHE). These find application in assorted optical problems. Particular cases of periodic solutions, where the elliptic function modulus equals 1, are various localized solutions of the CSHE. Each of these solutions exists for a certain relation between the parameters of the equation. As a result, they are particular cases of the complete set of periodic and localised solutions which may exist for this equation. In fact, they are multi-parameter families of solutions and they can serve as a seeding set of solutions which could be useful in other optical studies. We have also derived energy and momentum balance equations for the solutions of CSHE and checked that our stationary solutions satisfy the energy balance equation.

Original language | English |
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Pages (from-to) | 397-404 |

Number of pages | 8 |

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

Volume | 308 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - 2003 Mar 10 |

Externally published | Yes |

### Keywords

- Complex quintic Swift-Hohenberg equation
- Direct ansatz method
- Optical solitons

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

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

*308*(5-6), 397-404. https://doi.org/10.1016/S0375-9601(03)00080-X