Supratransmission-induced discrete rogue wave in nonlinear chain

Supratransmission-induced discrete rogue wave in nonlinear chain Alain Bertrand Togueu Motcheyo1, Masayuki Kimura2, Yusuke Doi3, Juan F. R. Archilla4 1Department of Mechanical Engineering, Higher Technical Teacher’s Training College (ENSET) Ebolowa, University of Ebolowa, P.O. Box 886, Ebolowa-Cameroon 2Department of Electrical and Electronic Engineering, Faculty of Science and Engineering,Setsunan University, Japan 3Department of Mechanical Engineering, Graduate School of Engineering, Osaka University 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan 4Group of Nonlinear Physics, Universidad de Sevilla, ETSI Informtica, Avda Reina Mercedes s/n, 41012-Sevilla, Spain Email: [email protected], [email protected], [email protected], [email protected] Abstract—We numerically generate a discrete rogue wave in a chain of a nonlinear pendulum using the nonlinear supratransmission way and the instability of shaken pendulum. This could open the way for the application of discrete rogue waves within simple devices. 1. Introduction Since the pioneering work by Geniet and L´ eon [1] on the nonlinear supratranmission phenomenon, the behavior of the plane wave in the forbidden band has fascinated several researchers. Nowadays, the nonlinear supratransmission phenomenon appears to be a way to generate travelling solitons such as symmetric (asymmetric) breather [2] and kink [3] to mention a few. Can rogue waves be generated by a nonlinear band gap transmission way? Answer this question is the aim of this work. 2. Mathematical description of the model Let us consider the equation of motion of the nth pendulum in the form[4, 5]: ¨ θn−c(θn+1+θn−1−2θn)+sin(θn)+fω2cos(ωτ) cos(θn)=0, (1) The numerical simulation of equation (1) submitted to the periodically driven edge and parametric excitation is given in figure 1. Acknowledgments A B Togueu Motcheyo would like to thank NOLTA2022 organizing committee members for the opportunity given to him to present this work. ORCID iDs ABTM: 0000-0002-6918-9281, MK: 0000-0002-1445- 6266, YD: 0000-0003-3749-5353, JFRA: 0000-0001-6583-6114 Figure 1: f=0.026; c=1; ω=0.95rad.s−1. References [1] F. Geniet and J. Leon, Energy transmission in the forbidden band gap of a nonlinear chain, Phys. Rev. Lett. 89, (2002) [2] E. Nkendji Kenkeu, A. B. Togueu Motcheyo, Thomas Kanaa and C. Tchawoua, Wave propagation with longitudinal dust grain oscillations in dusty plasma crystals, Phys. Plasmas 29, (2022) 043702. [3] A. B. Togueu Motcheyo, M. Kimura, Y. Doi and C. Tchawoua, Supratransmission in discrete onedimensional lattices with the cubic-quintic nonlinearity, Nonlinear Dyn 95, (2019) 2461. [4] J. Cuevas, L. Q. English, P. G. Kevrekidis, and M. Anderson, Discrete breathers in a forced-damped array of coupled pendula: modeling, computation, and experiment, Phys. Rev. Lett 102 (2009) 224101. [5] R. Basu Thakur, L. Q. English and A. J. Sievers, Driven intrinsic localized modes in a coupled pendulum array, J. Phys. D: Appl. Phys. 41 (2008) 015503. – 580 – 2022 International Symposium on Nonlinear Theory and Its Applications, NOLTA2022, Virtual, December 12-15, 2022 This work is licensed under a Creative Commons Attribution NonCommercial, No Derivatives 4.0 License.