Ablowitz-Ladik和离散非线性Schrödinger模型的接近性:Kuznetsov-Ma解的理论和数值研究

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Madison L. Lytle , Efstathios G. Charalampidis , Dionyssios Mantzavinos , Jesus Cuevas-Maraver , Panayotis G. Kevrekidis , Nikos I. Karachalios
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引用次数: 0

摘要

在这项工作中,我们研究了具有非零背景的时间周期解的形成,该解模拟了物理相关晶格非线性动力系统中的异常波,称为库兹涅佐夫-马(KM)呼吸子。从完全可积Ablowitz-Ladik (AL)模型出发,我们证明了KM初始数据的演化近似于不可积离散非线性Schrödinger (DNLS)方程在背景幅值和呼吸频率的某些参数值下的演化。这一发现促使我们研究两个模型的演化解之间的距离(在某些规范下),为此我们严格推导并在数值上确认了上界。最后,我们的研究得到了DNLS方程数值精确的km型呼吸解的双参数(背景振幅和频率)分岔分析的补充。除了本文报道的这些波形的稳定性分析外,这项工作还展示了在DNLS设置中可能出现的具有平坦背景的波形的潜在参数制度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the proximity of Ablowitz–Ladik and discrete nonlinear Schrödinger models: A theoretical and numerical study of Kuznetsov-Ma solutions
In this work, we investigate the formation of time-periodic solutions with a non-zero background that emulate rogue waves, known as Kuznetsov-Ma (KM) breathers, in physically relevant lattice nonlinear dynamical systems. Starting from the completely integrable Ablowitz–Ladik (AL) model, we demonstrate that the evolution of KM initial data is proximal to that of the non-integrable discrete Nonlinear Schrödinger (DNLS) equation for certain parameter values of the background amplitude and breather frequency. This finding prompts us to investigate the distance (in certain norms) between the evolved solutions of both models, for which we rigorously derive and numerically confirm an upper bound. Finally, our studies are complemented by a two-parameter (background amplitude and frequency) bifurcation analysis of numerically exact, KM-type breather solutions of the DNLS equation. Alongside the stability analysis of these waveforms reported herein, this work additionally showcases potential parameter regimes where such waveforms with a flat background may emerge in the DNLS setting.
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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