### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### 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

**Periodic and optical soliton solutions of the quintic complex Swift-Hohenberg equation.** / Ankiewicz, Adrian; Maruno, Kenichi; Akhmediev, Nail.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 308, no. 5-6, pp. 397-404. https://doi.org/10.1016/S0375-9601(03)00080-X

}

TY - JOUR

T1 - Periodic and optical soliton solutions of the quintic complex Swift-Hohenberg equation

AU - Ankiewicz, Adrian

AU - Maruno, Kenichi

AU - Akhmediev, Nail

PY - 2003/3/10

Y1 - 2003/3/10

N2 - 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.

AB - 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.

KW - Complex quintic Swift-Hohenberg equation

KW - Direct ansatz method

KW - Optical solitons

UR - http://www.scopus.com/inward/record.url?scp=0037429758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037429758&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(03)00080-X

DO - 10.1016/S0375-9601(03)00080-X

M3 - Article

AN - SCOPUS:0037429758

VL - 308

SP - 397

EP - 404

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 5-6

ER -