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DY: Fachverband Dynamik und Statistische Physik

DY 8: Focus Session: Nonlinear Dynamics and Stochastic Processes – Advances in Theory and Applications II

DY 8.3: Vortrag

Montag, 17. März 2025, 15:45–16:00, H43

Back to the future: Fermi--Pasta--Ulam--Tsingou recurrence in a time-delayed system — •Jonas Mayer Martins¹, Elias Koch¹, Julien Javaloyes², and Svetlana V. Gurevich¹ — ¹Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9 and Center for Nonlinear Science (CeNoS), University of Münster, Corrensstrasse 2, 48149 Münster, Germany — ²Departament de Física and IAC-3, Universitat de les Illes Balears, C/ Valldemossa km 7.5, 07122 Palma de Mallorca, Spain

We demonstrate Fermi--Pasta--Ulam--Tsingou (FPUT) recurrence, a surprising quasi-periodicity of certain spatially extended systems, in a time-delayed system. Although the bi-Riccati system that we study is not integrable, we find in the long-delay limit that its normal form is a partial differential equation approximating the integrable Korteweg--de Vries (KdV) equation, prominently known to exhibit FPUT recurrence. Our results underscore the analogy between spatially extended and time-delayed systems.

Keywords: delay; integrability; normal form; nonlinear dynamics; FPUT