https://doi.org/10.1140/epjp/s13360-020-01069-1
Regular Article
Modulational instabilities and chaotic-like behaviors in repulsive lattices
1
Complex Systems, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon
2
International Center for Complex Systems, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé I, Cameroon
3
Centre Africain d’Excellence en Technologies de l’Information et de la Communication, B.P.812, Yaoundé, Cameroon
4
Département des SF, Faculté des Mines et des Industries Pétrolieres, P.O. Box 46, Maroua, Cameroon
5
Max Planck Institute for the Physics of Complex Systems, Nothnitzer Strasse 38, 01187, Dreseden, Germany
6
The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586, Strada Costiera, II-34014, Trieste, Italy
Received:
19
July
2020
Accepted:
31
December
2020
Published online:
1
February
2021
In this paper, we study the dynamics of granular mediums. By comparing each grain of the medium with a ball, and the interaction between various balls like linear elastic interactions, we have established that the dynamics of the system of pendulum used by Fermi–Pasta–Ulam can be governed by a discrete nonlinear Schrödinger equation. Like second advanced, we also established under which conditions this system could be prone to a modulational instability. The long-time dynamics of modulated waves is examined using numerical simulations which are corroborated with analytical results leading to the generation of nonlinear modulated waves which have the shape of a soliton. At the end, we compare our results with what have been carried out previously.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
