The linear and nonlinear instability of the Akhmediev breather
| Autor: | Petr Georgievich Grinevich, Paolo Maria Santini |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Nonlinear instability
35Q55 70K44 76E30 78A60 Breather Generalization Applied Mathematics Fluid Dynamics (physics.flu-dyn) FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Pattern Formation and Solitons (nlin.PS) Mathematical Physics (math-ph) Physics - Fluid Dynamics Space (mathematics) Nonlinear Sciences - Pattern Formation and Solitons Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Akhmediev breathers anomalous waves recurrence focusing nonlinear Schrodinger equation linear and non-linear instability squared eigenfunctions Constant (mathematics) Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics Optics (physics.optics) Mathematics Mathematical physics Physics - Optics |
| Popis: | The Akhmediev breather (AB) and its M-soliton generalization $AB_M$ are exact solutions of the focusing NLS equation periodic in space and exponentially localized in time over the constant unstable background; they describe the appearance of $M$ unstable nonlinear modes and their interaction, and they are expected to play a relevant role in the theory of periodic anomalous (rogue) waves (AWs) in nature. It is rather well established that they are unstable with respect to small perturbations of the NLS equation. Concerning perturbations of these solutions within the NLS dynamics, there is the following common believe in the literature. Let the NLS background be unstable with respect to the first $N$ modes; then i) if the $M$ unstable modes of the $AB_M$ solution are strictly contained in this set ($M1$. Comment: 31 pages, 4 figures, Simplification of final formulas was made in this version |
| Databáze: | OpenAIRE |
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