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Nonlinear Sciences > Exactly Solvable and Integrable Systems

Title: Linear Instability of the Peregrine Breather: Numerical and Analytical Investigations

Abstract: We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By constructing solutions of the linearization of the nonlinear Schr\"odinger equation in terms of quadratic products of components of the eigenfunctions of the Zakharov-Shabat system, we show that the Peregrine breather is linearly unstable. A numerical study employing a highly accurate Chebychev pseudo-spectral integrator confirms exponential growth of random initial perturbations of the Peregrine breather.
Comments: 12 pages, 4 figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
MSC classes: 37K15, 76B15
Cite as: arXiv:1803.06584 [nlin.SI]
  (or arXiv:1803.06584v1 [nlin.SI] for this version)

Submission history

From: Annalisa Calini [view email]
[v1] Sat, 17 Mar 2018 22:55:50 GMT (483kb)