Hone, A.N.W. and Novikov, V.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.
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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.
|Uncontrolled keywords:||FINITE DEPTH; FLUIDS|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Judith Broom|
|Date Deposited:||19 Dec 2007 18:40|
|Last Modified:||11 Jan 2012 10:40|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/1013 (The current URI for this page, for reference purposes)|
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