Existence, stability and spatio-temporal dynamics of time-quasiperiodic solutions on a finite background in discrete nonlinear Schrödinger models

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
E.G. Charalampidis , G. James , J. Cuevas-Maraver , D. Hennig , N.I. Karachalios , P.G. Kevrekidis
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引用次数: 0

Abstract

In the present work we explore the potential of models of the discrete nonlinear Schrödinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously shown to exist in the vicinity of the anti-continuum, vanishing-coupling limit of the model. We then use numerical continuation to illustrate their persistence for finite coupling, as well as to explore their spectral stability. We obtain an intricate bifurcation diagram showing a progression of such solutions from simpler ones bearing single- and two-site excitations to more complex, multi-site ones with a direct connection of the branches of the self-focusing and self-defocusing nonlinear regime. We further probe the variation of the solutions obtained towards the limit of vanishing frequency for both signs of the nonlinearity. Our analysis is complemented by exploring the dynamics of the solutions via direct numerical simulations.

离散非线性薛定谔模型中有限背景上时间准周期解的存在性、稳定性和时空动态性
在本研究中,我们探索了离散非线性薛定谔(DNLS)模型在有限背景上支持空间局部和时间准周期解的潜力。这些解被严格证明存在于模型的反连续、消失耦合极限附近。然后,我们用数值延续来说明它们在有限耦合下的持久性,并探索它们的谱稳定性。我们得到了一个复杂的分岔图,显示了这些解的演进过程,从较简单的单点和双点激元,到较复杂的多点激元,以及自聚焦和自失焦非线性机制分支的直接连接。我们进一步探究了非线性的两种符号在频率消失极限时所获得的解的变化。我们的分析还通过直接数值模拟来探索解的动态变化。
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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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