Friedland L, Shagalov A G, Batalov S V
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Institute of Metal Physics, Ekaterinburg 620990, Russian Federation and Ural Federal University, Mira 19, Ekaterinburg 620002, Russian Federation.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042924. doi: 10.1103/PhysRevE.92.042924. Epub 2015 Oct 28.
Large amplitude traveling waves of the Korteweg-de-Vries (KdV) equation can be excited and controlled by a chirped frequency driving perturbation. The process involves capturing the wave into autoresonance (a continuous nonlinear synchronization) with the drive by passage through the linear resonance in the problem. The transition to autoresonance has a sharp threshold on the driving amplitude. In all previously studied autoresonant problems the threshold was found via a weakly nonlinear theory and scaled as α(3/4),α being the driving frequency chirp rate. It is shown that this scaling is violated in a long wavelength KdV limit because of the increased role of the nonlinearity in the problem. A fully nonlinear theory describing the phenomenon and applicable to all wavelengths is developed.
科特韦格 - 德弗里斯（KdV）方程的大幅行波可通过啁啾频率驱动微扰来激发和控制。该过程涉及通过问题中的线性共振使波与驱动进入自共振（一种连续的非线性同步）。向自共振的转变在驱动幅度上有一个尖锐的阈值。在所有先前研究的自共振问题中，阈值是通过弱非线性理论找到的，并且按α(3/4)缩放，α为驱动频率啁啾率。结果表明，由于问题中非线性作用的增强，在长波长KdV极限下这种缩放关系不成立。本文发展了一种描述该现象且适用于所有波长的完全非线性理论。
