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Russian-Chinese Conference «Integrable Systems and Geometry»
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The linear instability of the Akhmediev breather, the "missed" modes and the regular approach P. G. Grinevichabc, P. M. Santinide a Landau Institute for Theoretical Physics, USSR Academy of Sciences b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow d Department of Physics, University of Rome ``La Sapienza'' e Istituto Nazionale di Fisica Nucleare, Sezione di Roma |
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Abstract: The Akhmediev breathers are used in the literature as a mathematical model of anomalous (rogue) waves. For physical applications it is important to know if they are stable. Until recently, the common opinion in the literature was that these solutions are neutrally stable due to "saturation of instabilities" mechanism. We show that these solutions are unstable by explicitly constructing the "missed modes", i.e. exponentially growing in time solutions of the linearized equation. We also demonstrate how the unstable modes can be derived using a regular procedure. Language: English |
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