Recurrence in the high-order nonlinear Schrödinger equation: A low-dimensional analysis
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Updated: Feb 15, 2026

Protocol for Three-dimensional Confocal Morphometric Analysis of Astrocytes
Published on: December 11, 2015
Andrea Armaroli1, Maura Brunetti1, Jérôme Kasparian1
1GAP-Nonlinear, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland and ISE, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland.
Abstract:
We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deep-water waves (also named Dysthe equation). We validate the model by comparing it to numerical simulation; we distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model.
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