Explicit solutions of the reduced Ostrovsky equation |
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| Institution: | 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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