Hone, Andrew N.W.,
Novikov, Vladimir S.
(2004)
*
On a functional equation related to the intermediate long wave equation.
*
Journal of Physics A: Mathematical and General,
37
(32).
L399-L406.
ISSN 0305-4470.
(doi:10.1088/0305-4470/37/32/L02)
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Official URL http://dx.doi.org/10.1088/0305-4470/37/32/L02 |

## Abstract

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1088/0305-4470/37/32/L02 |

Uncontrolled keywords: | FINITE DEPTH; FLUIDS |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Andrew N W Hone |

Date Deposited: | 19 Dec 2007 18:40 UTC |

Last Modified: | 06 Feb 2020 04:00 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/1013 (The current URI for this page, for reference purposes) |

Hone, Andrew N.W.: | https://orcid.org/0000-0001-9780-7369 |

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