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On the Fermi-Pasta-Ulam-Tsingou recurrence of anomalous (rogue) waves in partial differential equations of nonlinear Schrödinger type
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DOI：10.1016/j.mechrescom.2026.104639.png)
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Abstract
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Anomalous (rogue) waves (AWs) are extreme waves of anomalously large amplitude with respect to the surrounding waves, arising apparently from nowhere and disappearing without leaving any trace. The simplest model describing the generation of AWs, due to modulation instability (MI) in nonlinear media, is the integrable self-focusing Nonlinear Schr & ouml;dinger (NLS) equation in 1+1 dimensions. In the space periodic setting, the appearance of NLS AWs is a recurring phenomenon and, in the simplest case of a single unstable mode, this recurrence is a Fermi-Pasta-Ulam-Tsingou (FPUT) type recurrence of linear and nonlinear stages of MI. In this paper we review some of the basic properties of the AW recurrence of FPUT-type in integrable and non integrable partial differential equations of NLS type in 1 + 1 and 2 + 1 dimensions.
Keywords:
FPUT recurrence
Periodic anomalous (rogue) waves
Nonlinear Schr & ouml
dinger type equations
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