On hierarchies of equations for the Benjamin-Ono equation |
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| Institution: | 1. Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA;2. Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar;3. Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia;1. Max-Planck-Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany;2. Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany;3. Department of Mathematical Physics, Toyama Prefectural University, Kurokawa 5180, Imizu, Toyama, 939-0398, Japan;1. University College London, UK;2. School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, Scotland, EH9 3FD, UK;3. Faculty of Health, Engineering and Sciences, University of Southern Queensland, Toowoomba, QLD, 4350, Australia;4. Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia;1. National Research Centre Kurchatov Institute, 123182 Moscow, Russia;2. Kaliningrad Branch, Moscow State University of Railways, 236039 Kaliningrad, Russia |
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| Abstract: | Two hierarchies of the Benjamin-Ono equation and their Lax pairs are derived by an algebraic approach. The hierarchies are proved to be the isospectral flows and non-isospectral flows and the corresponding time evolutions of the scattering data are obtained, thus the inverse scattering transform can be applied to solve them. |
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