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On a functional equation related to the intermediate long wave equation

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) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:1013)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
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 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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