Abstract : There are various spatially discrete nonlinear media in nature and engineering systems as diverse as solid crystal, metamaterial, and optical waveguide array, etc. Such media are mathematically modeled by nonlinear lattice dynamical systems. In both of experimental and mathematical systems, nonlinear localized waves such as solitons and discrete breathers are widely observed. The nonlinear localized waves have attracted much interest from the point of view of applied mathematics and that of physics problems such as thermalization and charge transport. So, mathematical and/or numerical analyses have been actively made. This MS aims at sharing and discussing recent results on the topic.
[00658] Existence of multi-pulse discrete breathers in Fermi-Pasta-Ulam-Tsingou lattices
Format : Talk at Waseda University
Author(s) :
Kazuyuki Yoshimura (Tottori University)
Abstract : Discrete breathers are spatially localized periodic solutions in nonlinear lattices. We prove the existence of odd symmetric, even symmetric, and multi-pulse discrete breathers in strong localization regime in one-dimensional infinite Fermi-Pasta-Ulam-Tsingou (FPUT) lattices with even interaction potentials. The multi-pulse discrete breather consists of an arbitrary number of the odd-like and/or even-like primary discrete breathers located separately on the lattice. The proof applies to both cases of pure attractive and repulsive-attractive interaction potentials.
[01557] Spectral properties of nonlinear excitations in semiclassical systems with charge transport
Format : Online Talk on Zoom
Author(s) :
Juan FR Archilla (Universidad de Sevilla)
Janis Bajars (University of Latvia)
Yusuke Doi (Osaka University)
Masayuki Kimura (Setsunan University)
Abstract : We study the spectral properties of polarobreathers, that is, breathers carrying charge in a semi-classical model. Lattice particles are described mathematically, while the charged particle is described as a quantum one within the tight-binding approximation. Three different spectra are considered: the spectra of the atom positions, the spectra of the charge carrier probability and the spectra of charge carrier probability amplitude. The observed spectrum properties are related with the physical properties of the semiclassical system.
[01269] Nonlinear waves in multistable mechanical metamaterials
Vincent Tournat (Institut d'Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université)
Jordan R. Raney (University of Pennsylvania)
Abstract : We explore collision behaviors of nonlinear waves in a multistable mechanical system with coupling between translational and rotational degrees of freedom. We show that the system can support two different types of nonlinear waves, specifically elastic vector solitons and topological solitons. Moreover, we experimentally and numerically demonstrate the nucleation of topological solitons via collisions of vector solitons. Our findings show a new potential way of generating and controlling nonlinear waves in a mechanical structure.
[01230] Soliton billiards
Format : Online Talk on Zoom
Author(s) :
Jesus Cuevas-Maraver (University of Seville)
Abstract : A point particle elastically reflected within an enclosed 2D domain is known as a billiard. Depending on the features of this domain, the trajectory of the particle can be closed or ergodic. In this talk, we show the similarities and differences when, instead of a classical particle, a soliton is scattered from closed 2D potentials. To this aim, we have considered a 2D NLS equation with saturable nonlinearity and square barriers (among other potentials).
00342 (2/2) : 4E @F308 [Chair: Kazuyuki Yoshimura]
[00812] Universality Classes for Nonlinear Wave Thermalization
Format : Talk at Waseda University
Author(s) :
Sergej Flach (Institute for Basic Science)
Abstract : We study the slowing down of thermalization of many-body dynamical systems upon approaching integrable limits. We identify two fundamentally distinct long-range and short-range classes. The long-range class results in a single parameter scaling of the Lyapunov spectrum, with the rescaled spectrum approaching an analytical function. The short-range class results in a rescaled Lyapunov spectrum approaching a non-analytic function through an exponential suppression of all Lyapunov exponents relative to the largest one.
[01278] Numerical experiment on nonlinear localized oscillation propagating in a mass-spring chain
Format : Talk at Waseda University
Author(s) :
Yosuke Watanabe (Setsunan University)
Yusuke Doi (Osaka University)
Abstract : Nonlinear localized oscillations excited and propagated in a mass-spring chain are studied. Letting the mass at one end of the chain driven sinusoidally at high frequency and large amplitude, localized oscillations can be excited intermittently near the end and propagated down the chain one after another at a constant speed. This phenomenon is known as supratransmission. We have experimentally observed the supratransmission by a mechanical mass-spring chain which emulates the Fermi-Pasta-Ulam one of beta type. The experimental results are compared with the numerical ones.
[01274] Moving Intrinsic Localized Modes Created by Transforming Wavenumber-frequency Spectrum of a Static Intrinsic Localized Mode in FPUT-NKG Mixed Lattices
Format : Talk at Waseda University
Author(s) :
Masayuki Kimura (Setsunan University)
Kosuke Kawasaki (Kyoto University)
Shinji Doi (Kyoto University)
Abstract : Intrinsic localized mode $($ILM$)$, also known as discrete breather $($DB$)$, is a spatially localized vibration in nonlinear lattices. It is well known that ILM can travel the lattices without decay of energy localization for a long period of time. In this study, initial values of moving ILMs with arbitrary speed are created by transforming the wavenumber-frequency spectrum of a static ILM. We will discuss the characteristics of the created moving ILMs.
[00992] Structure of pairwise interaction symmetric lattice for moving discrete breather
Format : Talk at Waseda University
Author(s) :
Yusuke Doi (Osaka University)
Kazuyuki Yoshimura (Tottori University)
Abstract : The mobility of discrete breathers is an essential issue from the viewpoint of energy transport in microstructure and nanostructures. In this presentation, we construct a nonlinear lattice with long-range interaction, which supports the smooth mobility of the discrete breather by considering the invariance of the interaction potential to a certain mapping corresponding to the translational manipulation of the waveform. Numerical results on the dynamics of the discrete breather in the constructed lattice are also presented.
