Kimmoun O, Hsu H C, Branger H, Li M S, Chen Y Y, Kharif C, Onorato M, Kelleher E J R, Kibler B, Akhmediev N, Chabchoub A
Aix-Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France.
Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan.
Sci Rep. 2016 Jul 20;6:28516. doi: 10.1038/srep28516.
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. One prominent form of instability in a distributed system is its response to a harmonic modulation. Such instability has special names in various branches of physics and is generally known as modulation instability (MI). The MI leads to a growth-decay cycle of unstable waves and is therefore related to Fermi-Pasta-Ulam (FPU) recurrence since breather solutions of the nonlinear Schrödinger equation (NLSE) are known to accurately describe growth and decay of modulationally unstable waves in conservative systems. Here, we report theoretical, numerical and experimental evidence of the effect of dissipation on FPU cycles in a super wave tank, namely their shift in a determined order. In showing that ideal NLSE breather solutions can describe such dissipative nonlinear dynamics, our results may impact the interpretation of a wide range of new physics scenarios.
不稳定性是自然界中经常观察到的常见现象，有时会在看似正常的情况下导致意想不到的灾难。分布式系统中一种突出的不稳定性形式是其对谐波调制的响应。这种不稳定性在物理学的各个分支中有特定的名称，通常被称为调制不稳定性（MI）。MI导致不稳定波的增长 - 衰减周期，因此与费米 - 帕斯塔 - 乌拉姆（FPU）递归有关，因为已知非线性薛定谔方程（NLSE）的呼吸子解能够准确描述保守系统中调制不稳定波的增长和衰减。在这里，我们报告了关于超波槽中耗散对FPU周期影响的理论、数值和实验证据，即它们按确定顺序的偏移。在表明理想的NLSE呼吸子解可以描述这种耗散非线性动力学时，我们的结果可能会影响对广泛的新物理场景的解释。
