Rogue-wave solutions of the Zakharov equation |
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Authors: | Jiguang Rao Lihong Wang Wei Liu Jingsong He |
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Institution: | 1.Mathematics Department, Faculty of Science,Ningbo University,Ningbo,China;2.Faculty of Mechanical Engineering & Mechanics,Ningbo University,Ningbo,China;3.School of Mathematical Sciences,University of Science and Technology of China,Hefei,China |
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Abstract: | Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane (x, y) arising from a constant background at t ? 0 and then gradually tending to the constant background for t ? 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey–Stewartson equation analytically and graphically. |
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