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Emerging structures at the linear stage of evolution of an unstable dispersive modulated wave field

Evgeny Mogilevskiy*

Lev Shemer†

  • *Contact author: emogilevskiy@tauex.tau.ac.il; evgenym@ariel.ac.il
  • †Contact author: shemerl@tauex.tau.ac.il
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Phys. Rev. Research 8, 043071 – Published 19 October, 2026

DOI: https://doi.org/10.1103/fstd-8wwj

Abstract

We study the spatiotemporal evolution of small disturbances developing in an unstable dispersive system. At the initial linear stage, the slow modulation of an unstable harmonic is analyzed subject to prescribed initial and boundary conditions. A theoretical model based on a modified linearized Ginzburg-Landau equation predicts the emergence of effectively localized envelope structures that can strongly affect the subsequent nonlinear stage of evolution and provides a simple criterion for the onset of absolute instability. As an illustrative example, we consider wind waves generated by an impulsive forcing in a semi-infinite domain over a viscous shear flow.

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Phys. Rev. Research 8, 043071– Published 19 October, 2026
  • Received 8 March 2026
  • Accepted 5 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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