标题： 弱非线性波系统与单模激励 显示英文标题

标题： Weakly nonlinear wave systems with a single mode excitation

摘要： 一种由于单模激发而可能发生的弱非线性波相互作用的新模型（D模型）被提出。 它能够在单一的理论框架中再现各种非线性波现象，如间歇性和离散及连续能量谱。 形成D级联的条件、离散和连续能量D级联的方向、D级联终止的条件等，都是从初始状态直接得出的结果。 不需要统计假设，因为所有效应都是通过不同模态的相互作用得出的。 在给出的例子中——具有小非线性的重力表面波$\o^2=g\,k$——D模型预测了Benjamin-Feir不稳定性侧带的不对称增长；从离散到连续能量谱的转变导致了饱和的Phillips功率谱$\sim g^2\o^{-5}$，这是对初始激发参数特定选择的结果。 D模型可以应用于流体力学、非线性光学、电动力学、对流理论等中出现的众多弱非线性波系统的实验和理论研究。 显示英文摘要

摘要： A novel model (D-model) of weakly nonlinear wave interactions possible due to a singly mode excitation is presented. It allows to reproduce in a single theoretical frame various nonlinear wave phenomena such as intermittency and discrete and continuous energy spectra. Conditions for the formation of a D-cascade, direction of discrete and continuous energy D-cascades, conditions for D-cascade termination, etc. are obtained as a direct outcome from the initial state. No statistical assumptions are needed as all effects are derived from the interaction of distinct modes. In the example given -- gravity surface waves $\o^2=g\,k$ with small nonlinearity -- D-model predicts asymmetrical growth of side-bands for Benjamin-Feir instability; transition from discrete to continuous energy spectrum yields the saturated Phillips' power spectrum $\sim g^2\o^{-5}$, for specific choice of the parameters of initial excitation. D-model can be applied to the experimental and theoretical study of numerous weakly nonlinear wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, convection theory, etc.