How close are integrable and nonintegrable models: A parametric case study based on the Salerno model
How close are integrable and nonintegrable models: A parametric case study based on the Salerno model
复制标题
可积模型和不可积模型有多接近：基于萨莱诺模型的参数化案例研究
DOI：
10.1103/physreve.107.024202
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发表时间：
2023
影响因子：
2.4
通讯作者：
Kevrekidis, Panayotis G.
中科院分区：
文献类型：
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作者：
Mithun, Thudiyangal;Maluckov, Aleksandra;Mančić, Ana;Khare, Avinash;Kevrekidis, Panayotis G.
在目前的工作中，我们回顾了Salerno模型，它是一个在著名的可积系统(Ablwitz-Ladik格子)和实验上易处理的不可积系统(离散的非线性薛定谔模型)之间进行内插的原型系统。我们要问的问题是，对于“通用的”初始数据，可积与不可积模型有多接近？我们对这个问题更精确的表述是，在不可积的情况下，以前守恒量的不变性保持得有多好？通过研究这一点，我们发现，在Salerno模型的情况下，通过测量这些以前守恒量，甚至可以敏感地感觉到与可积性的微小偏差。然而，考虑到这些量的知识需要对系统进行深入的物理和数学分析，我们寻求一种更“通用”的诊断方法来说明可积性破坏的表现。我们认为，基于我们的Salerno模型计算，李亚普诺夫指数的全谱可能是对这一影响的敏感诊断。
In the present work we revisit the Salerno model as a prototypical system that interpolates between a well-known integrable system (the Ablowitz-Ladik lattice) and an experimentally tractable, nonintegrable one (the discrete nonlinear Schrödinger model). The question we ask is, for “generic” initial data, how close are the integrable to the nonintegrable models? Our more precise formulation of this question is, How well is the constancy of formerly conserved quantities preserved in the nonintegrable case? Upon examining this, we find that even slight deviations from integrability can be sensitively felt by measuring these formerly conserved quantities in the case of the Salerno model. However, given that the knowledge of these quantities requires a deep physical and mathematical analysis of the system, we seek a more “generic” diagnostic towards a manifestation of integrability breaking. We argue, based on our Salerno model computations, that the full spectrum of Lyapunov exponents could be a sensitive diagnostic to that effect.