Propagating wave patterns and “peakons” of the Davey–Stewartson system |
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| Institution: | 1. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk, Cairo, Egypt;2. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey;3. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL-35762-7500, USA;4. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;5. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;6. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar |
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| Abstract: | Two exact, doubly periodic, propagating wave patterns of the Davey–Stewartson system are computed analytically by a special separation of variables procedure. For the first solution there is a cluster of smaller peaks within each period. The second one consists of a rectangular array of ‘plates’ joined together by sharp edges, and is thus a kind of ‘peakons’ for this system of (2 + 1) (2 spatial and 1 temporal) dimensional evolution equations. A long wave limit will yield exponentially localized waves different from the conventional dromion. The stability properties and nonlinear dynamics must await further investigations. |
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