Gradient catastrophe and Peregrine soliton in nonlinear flexible mechanical metamaterials

Fuente: arXiv
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Autores principales: Demiquel, Antoine, Achilleos, Vassos, Theocharis, Georgios, Tournat, Vincent
Formato: Preprint
Publicado: 2025
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author Demiquel, Antoine
Achilleos, Vassos
Theocharis, Georgios
Tournat, Vincent
author_facet Demiquel, Antoine
Achilleos, Vassos
Theocharis, Georgios
Tournat, Vincent
contents We explore the generation of extreme wave events in mechanical metamaterials using the regularization of the gradient catastrophe theory developed by A. Tovbis and M. Bertola for the nonlinear Schrödinger equation. According to this theory, Peregrine solitons can locally emerge in the semiclassical limit of the nonlinear Schrödinger equation. Our objective is to determine whether the phenomenon of gradient catastrophe can occur in a class of architected structures designated as flexible mechanical metamaterials, both with and without losses. We demonstrate theoretically and numerically that this phenomenon can occur in a canonical example of such flexible mechanical metamaterial, a chain of rotating units, studied earlier for its ability to support robust nonlinear waves such as elastic vector solitons. We find that in the presence of weak losses, the gradient catastrophe persists although the amplitude of extreme generated events is smaller and their onset is delayed compared to the lossless configuration.
format Preprint
id arxiv_https___arxiv_org_abs_2503_23836
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gradient catastrophe and Peregrine soliton in nonlinear flexible mechanical metamaterials
Demiquel, Antoine
Achilleos, Vassos
Theocharis, Georgios
Tournat, Vincent
Pattern Formation and Solitons
Classical Physics
We explore the generation of extreme wave events in mechanical metamaterials using the regularization of the gradient catastrophe theory developed by A. Tovbis and M. Bertola for the nonlinear Schrödinger equation. According to this theory, Peregrine solitons can locally emerge in the semiclassical limit of the nonlinear Schrödinger equation. Our objective is to determine whether the phenomenon of gradient catastrophe can occur in a class of architected structures designated as flexible mechanical metamaterials, both with and without losses. We demonstrate theoretically and numerically that this phenomenon can occur in a canonical example of such flexible mechanical metamaterial, a chain of rotating units, studied earlier for its ability to support robust nonlinear waves such as elastic vector solitons. We find that in the presence of weak losses, the gradient catastrophe persists although the amplitude of extreme generated events is smaller and their onset is delayed compared to the lossless configuration.
title Gradient catastrophe and Peregrine soliton in nonlinear flexible mechanical metamaterials
topic Pattern Formation and Solitons
Classical Physics
url https://arxiv.org/abs/2503.23836