On the discrete Kuznetsov–Ma solutions for the defocusing Ablowitz–Ladik equation with large background amplitude

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2025-01-23 DOI:10.1016/j.wavemoti.2025.103496

E.C. Boadi , E.G. Charalampidis , P.G. Kevrekidis , N.J. Ossi , B. Prinari

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引用次数: 0

Abstract

The focus of this work is on a class of solutions of the defocusing Ablowitz–Ladik lattice on an arbitrarily large background which are discrete analogs of the Kuznetsov–Ma (KM) breathers of the focusing nonlinear Schrödinger equation. One such solution was obtained in 2019 as a byproduct of the Inverse Scattering Transform, and it was observed that the solution could be regular for certain choices of the soliton parameters, but its regularity was not analyzed in detail. This work provides a systematic investigation of the conditions on the background and on the spectral parameters that guarantee the KM solution to be non-singular on the lattice for all times. Furthermore, a novel KM-type breather solution is presented which is also regular on the lattice under the same conditions. We also employ Darboux transformations to obtain a multi-KM breather solution, and show that parameters choices exist for which a double KM breather solution is regular on the lattice. We analyze the features of these solutions, including their frequency which, when tending to 0, renders them proximal to rogue waveforms. Finally, numerical results on the stability and spatio-temporal dynamics of the single KM breathers are presented, showcasing the potential destabilization of the obtained states due to the modulational instability of their background.

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大背景幅值离焦Ablowitz-Ladik方程的离散Kuznetsov-Ma解

本文研究了任意大背景下散焦Ablowitz-Ladik晶格的一类解，它们是聚焦非线性Schrödinger方程的Kuznetsov-Ma （KM）呼吸方程的离散类似物。2019年，作为逆散射变换的副产物，获得了一个这样的解，并观察到该解对于某些孤子参数的选择可能是规则的，但没有详细分析其规律性。本文系统地研究了保证KM解在晶格上始终非奇异的背景条件和谱参数。在此基础上，提出了一种新的km型呼吸解，该解在相同条件下在格上也是正则的。我们还利用Darboux变换得到了一个多KM呼吸解，并证明了存在双KM呼吸解在格上是正则的参数选择。我们分析了这些解的特征，包括它们的频率，当趋向于0时，使它们接近于异常波形。最后，给出了单个KM呼吸器的稳定性和时空动力学的数值结果，显示了由于其背景的调制不稳定性而获得的状态的潜在不稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.