论文标题
非线性动力学中的复杂的包络变量近似
Complex Envelope Variable Approximation in Nonlinear Dynamics
论文作者
论文摘要
我们将复杂的包络变量近似（CEVA）表示为分析基本非线性动力学系统的非常有用且紧凑的方法。即使在初始问题中没有任何小参数时，它也使我们可以研究固定和非平稳动态。值得注意的是，CEVA在离散系统中对非线性正常模式及其共振相互作用进行分析，而没有对振荡幅度的任何限制。在本文中，我们制定了CEVA的形式主义，并证明了其应用的一些非平凡示例。简要讨论了该方法的优势和可能的问题。
We present the Complex Envelope Variable Approximation (CEVA) as the very useful and compact method for the analysis of the essentially nonlinear dynamical systems. It allows us to study both the stationary and non-stationary dynamics even in the cases, when any small parameters are absent in the initial problem. It is notable that the CEVA admits the analysis of the nonlinear normal modes and their resonant interactions in the discrete systems without any restrictions on the oscillation amplitudes. In this paper we formulate the CEVA's formalism and demonstrate some non-trivial examples of its application. The advantages of the method and possible problems are briefly discussed.
