It is shown that the Vakhnenko equation (VE) and the Ostrovsky-Hunter equation (OHE) are particular forms of the reduced Ostrovsky equation, and that they are related by a simple transformation. Explicit analytical periodic and solitary travelling-wave solutions of the OHE are derived by using a method used previously by Vakhnenko and the present author to solve the VE. These exact solutions of the OHE are related to some approximate solutions obtained by Boyd [Boyd JP. Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves). Eur J Appl Math 2005;15:1-17].
- chaos theory
- vakhnenko equation