### Abstract

Original language | English |
---|---|

Number of pages | 17 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications |

Volume | 4 |

Issue number | 053 |

Publication status | Published - 2008 |

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### Keywords

- Ostrovsky equation
- Ostrovsky–Hunter equation
- Vakhnenko equation
- periodic waves
- solitary waves
- corner waves
- cuspons
- loops

### Cite this

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*Symmetry, Integrability and Geometry: Methods and Applications*, vol. 4, no. 053.

**Periodic and solitary-wave solutions of an extended reduced Ostrovsky equation.** / Parkes, E. John.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Periodic and solitary-wave solutions of an extended reduced Ostrovsky equation

AU - Parkes, E. John

PY - 2008

Y1 - 2008

N2 - Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of constant parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be a smooth hump, a cuspon, a loop or a parabolic wave with compact support. All the solutions are expressed in parametric form. Only in one circumstance can the variable parameter be eliminated to give a solution in explicit form. In this case the resulting waves are either a solitary parabolic wave with compact support or the corresponding periodic corner waves.

AB - Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination of constant parameters. The periodic waves may be smooth humps, cuspons, loops or parabolic corner waves. The latter are shown to be the maximum-amplitude limit of a one-parameter family of periodic smooth-hump waves. The solitary waves may be a smooth hump, a cuspon, a loop or a parabolic wave with compact support. All the solutions are expressed in parametric form. Only in one circumstance can the variable parameter be eliminated to give a solution in explicit form. In this case the resulting waves are either a solitary parabolic wave with compact support or the corresponding periodic corner waves.

KW - Ostrovsky equation

KW - Ostrovsky–Hunter equation

KW - Vakhnenko equation

KW - periodic waves

KW - solitary waves

KW - corner waves

KW - cuspons

KW - loops

UR - http://www.emis.de/journals/SIGMA/

UR - http://www.emis.de/journals/SIGMA/2008/053/sigma08-053.pdf

M3 - Article

VL - 4

JO - Symmetry, Integrability and Geometry: Methods and Applications

JF - Symmetry, Integrability and Geometry: Methods and Applications

SN - 1815-0659

IS - 053

ER -