Explicit solutions of the reduced Ostrovsky equation |
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| Affiliation: | 1. Department of Applied Physics, Hokkaido University, N13W8 Kita-ku, Sapporo, 060-8628, Japan;2. Japan Science and Technology Agency, CREST, 5, Sanbancho, Chiyoda-ku, Tokyo 102-0075, Japan;1. School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, PR China;2. School of Science, Beijing Technology and Business University, Beijing 100048, PR China;3. Beijing Key Laboratory of Big Data Technology for Food Safety, Beijing 100048, PR China;1. NOAA Earth Science Research Laboratory, United States;2. University of Colorado, Boulder, United States;3. University of Southern Queensland, Toowoomba, Australia;4. Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia;1. Institut d’Electronique Fondamentale, Université Paris-Sud, CNRS, UMR 8622, F-91405 Orsay, France;2. Lycée Jacques Prévert, F-27500 Pont-Audemer, France;3. Russian Quantum Center, 100 Novaya Street, Skolkovo, Moscow region 143025, Russia;4. Laboratoire Interdisciplinaire des Energies de Demain (LIED), UMR 8236 Université Paris Diderot, CNRS, 5 Rue Thomas Mann, 75013 Paris, France;1. E.T.S. Ingeniería Industrial, Universidad de Málaga, Dr Ortiz Ramos s/n, 29071 Málaga, Spain;2. Dept. Mecánica, Esc. Pol. Superior, Universidad de Córdoba, Campus de Rabanales, 14071 Córdoba, Spain |
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| Abstract: | 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]. |
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