LETTER TO THE EDITOR: On a functional equation related to the intermediate long wave equation
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 BenjaminOno equation are the unique integrable cases within a particular class of integrodifferential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 2004
 DOI:
 10.1088/03054470/37/32/L02
 Bibcode:
 2004JPhA...37L.399H