On the proximity of Ablowitz–Ladik and discrete nonlinear Schrödinger models: A theoretical and numerical study of Kuznetsov-Ma solutions

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2025-03-30 DOI:10.1016/j.wavemoti.2025.103547

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

Abstract

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 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.