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Starosvetsky Y, Arbel R. Transient traveling breather response of strongly anharmonic array of self-sustained oscillators: Analytical study. Phys Rev E 2024; 109:024222. [PMID: 38491678 DOI: 10.1103/physreve.109.024222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2023] [Accepted: 01/03/2024] [Indexed: 03/18/2024]
Abstract
In the present study, we analyze the transient response of a locally excited chain of strongly anharmonic self-sustained oscillators. This discrete system under consideration models the dynamics of genuinely nonlinear, aeroelastic metamaterial. We particularly focus on the transient evolution of the traveling dissipative breathers, forming in locally excited, finite chains of self-sustained oscillators. The genuinely anharmonic nature of the system under consideration turns the asymptotic analysis of the transient regimes arising in this type of model into a highly challenging task. In the present study, we formulate a special analytical approach which allows for a simple, explicit, and fairly accurate analytical description of the amplitude evolution of the breather core towards the steady state as well as its instantaneous position.
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Affiliation(s)
- Y Starosvetsky
- Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa 32000, Israel
| | - R Arbel
- Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa 32000, Israel
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Sato M, Furusawa H, Sakai M, Soga Y, Sievers AJ. Experimental study of intrinsic localized mode mobility in a cyclic, balanced, 1D nonlinear transmission line. CHAOS (WOODBURY, N.Y.) 2023; 33:073149. [PMID: 37486665 DOI: 10.1063/5.0156547] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Accepted: 07/04/2023] [Indexed: 07/25/2023]
Abstract
Mobile intrinsic localized modes (ILMs) in balanced nonlinear capacitive-inductive cyclic transmission lines are studied by experiment, using a spatiotemporal driver under damped steady-state conditions. Without nonlinear balance, the experimentally observed resonance between the traveling ILM and normal modes of the nonlinear transmission line generates lattice drag via the production of a lattice backwave. In our experimental study of a balanced running ILM in a steady state, it is observed that the fundamental resonance can be removed over extended, well-defined driving frequency intervals and strongly suppressed over the complete ILM driving frequency range. Because both of these nonlinear capacitive and inductive elements display hysteresis our observation demonstrates that the experimental system, which is only partially self-dual, is surprisingly tolerant, regarding the precision necessary to eliminate the ILM backwave. It appears that simply balancing the cell dual nonlinearities makes the ILM envelope shape essentially the same at the two locations in the cell, so that the effective lattice discreteness seen by the ILM nearly vanishes.
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Affiliation(s)
- M Sato
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - H Furusawa
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - M Sakai
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - Y Soga
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - A J Sievers
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA
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Sato M, Furusawa H, Soga Y, Sievers AJ. Propagating intrinsic localized mode in a cyclic, dissipative, self-dual one-dimensional nonlinear transmission line. Phys Rev E 2023; 107:034202. [PMID: 37072939 DOI: 10.1103/physreve.107.034202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 02/14/2023] [Indexed: 04/20/2023]
Abstract
A well-known feature of a propagating localized excitation in a discrete lattice is the generation of a backwave in the extended normal mode spectrum. To quantify the parameter-dependent amplitude of such a backwave, the properties of a running intrinsic localized mode (ILM) in electric, cyclic, dissipative, nonlinear 1D transmission lines, containing balanced nonlinear capacitive and inductive terms, are studied via simulations. Both balanced and unbalanced damping and driving conditions are treated. The introduction of a unit cell duplex driver, with a voltage source driving the nonlinear capacitor and a synchronized current source, the nonlinear inductor, provides an opportunity to design a cyclic, dissipative self-dual nonlinear transmission line. When the self-dual conditions are satisfied, the dynamical voltage and current equations of motion within a cell become the same, the strength of the fundamental, resonant coupling between the ILM and the lattice modes collapses, and the associated fundamental backwave is no longer observed.
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Affiliation(s)
- M Sato
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - H Furusawa
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - Y Soga
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - A J Sievers
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA
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Muniz ALM, Wimmer M, Bisianov A, Peschel U, Morandotti R, Jung PS, Christodoulides DN. 2D Solitons in PT-Symmetric Photonic Lattices. PHYSICAL REVIEW LETTERS 2019; 123:253903. [PMID: 31922782 DOI: 10.1103/physrevlett.123.253903] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Indexed: 06/10/2023]
Abstract
Over the last few years, parity-time (PT) symmetry has been the focus of considerable attention. Ever since, pseudo-Hermitian notions have permeated a number of fields ranging from optics to atomic and topological physics, as well as optomechanics, to mention a few. Unlike their Hermitian counterparts, nonconservative systems do not exhibit a priori real eigenvalues and hence unitary evolution. However, once PT symmetry is introduced, such dissipative systems can surprisingly display a real eigenspectrum, thus ensuring energy conservation during evolution. In optics, PT symmetry can be readily established by incorporating, in a balanced way, regions having an equal amount of optical gain and loss. However, thus far, all optical realizations of such PT symmetry have been restricted to a single transverse dimension (1D), such as arrays of optical waveguides or active coupled cavity arrangements. In most cases, only the loss function was modulated-a restrictive aspect that is only appropriate for linear systems. Here, we present an experimental platform for investigating the interplay between PT symmetry and nonlinearity in two-dimensional (2D) environments, where nonlinear localization and soliton formation can be observed. In contrast to typical dissipative solitons, we demonstrate a one-parameter family of soliton solutions that are capable of displaying attributes similar to those encountered in nonlinear conservative arrangements. For high optical powers, this new family of PT solitons tends to collapse on a discrete network-thus giving rise to an amplified, self-accelerating structure.
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Affiliation(s)
- Andre L M Muniz
- Abbe Center of Photonics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Martin Wimmer
- Abbe Center of Photonics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Arstan Bisianov
- Abbe Center of Photonics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Ulf Peschel
- Abbe Center of Photonics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | | | - Pawel S Jung
- CREOL, University of Central Florida, Orlando, Florida 32816-2700, USA
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Abdullaev FK, Salerno M. Dissipative solitons in the discrete Ginzburg-Landau equation with saturable nonlinearity. Phys Rev E 2018; 97:052208. [PMID: 29906973 DOI: 10.1103/physreve.97.052208] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2018] [Indexed: 11/07/2022]
Abstract
The modulational instability of nonlinear plane waves and the existence of periodic and localized dissipative solitons and waves of the discrete Ginzburg-Landau equation with saturable nonlinearity are investigated. Explicit analytic expressions for periodic solutions with a zero and a finite background are derived and their stability properties investigated by means of direct numerical simulations. We find that while discrete periodic waves and solitons on a zero background are stable under time evolution, they may become modulationally unstable on finite backgrounds. The effects of a linear ramp potential on stable localized dissipative solitons are also briefly discussed.
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Affiliation(s)
| | - Mario Salerno
- Dipartimento di Fisica E.R. Caianiello and INFN, Gruppo Collegato di Salerno, Universita di Salerno, Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
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Gninzanlong CL, Ndjomatchoua FT, Tchawoua C. Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy. CHAOS (WOODBURY, N.Y.) 2018; 28:043105. [PMID: 31906659 DOI: 10.1063/1.5009147] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.
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Affiliation(s)
| | | | - Clément Tchawoua
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Yaoundé, Cameroon
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Sato M, Nakaguchi T, Ishikawa T, Shige S, Soga Y, Doi Y, Sievers AJ. Supertransmission channel for an intrinsic localized mode in a one-dimensional nonlinear physical lattice. CHAOS (WOODBURY, N.Y.) 2015; 25:103122. [PMID: 26520088 DOI: 10.1063/1.4933329] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
It is well known that a moving intrinsic localized mode (ILM) in a nonlinear physical lattice looses energy because of the resonance between it and the underlying small amplitude plane wave spectrum. By exploring the Fourier transform (FT) properties of the nonlinear force of a running ILM in a driven and damped 1D nonlinear lattice, as described by a 2D wavenumber and frequency map, we quantify the magnitude of the resonance where the small amplitude normal mode dispersion curve and the FT amplitude components of the ILM intersect. We show that for a traveling ILM characterized by a specific frequency and wavenumber, either inside or outside the plane wave spectrum, and for situations where both onsite and intersite nonlinearity occur, either of the hard or soft type, the strength of this resonance depends on the specific mix of the two nonlinearities. Examples are presented demonstrating that by engineering this mix the resonance can be greatly reduced. The end result is a supertransmission channel for either a driven or undriven ILM in a nonintegrable, nonlinear yet physical lattice.
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Affiliation(s)
- M Sato
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - T Nakaguchi
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - T Ishikawa
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - S Shige
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - Y Soga
- Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan
| | - Y Doi
- Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan
| | - A J Sievers
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA
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