电动系统的非线性简正模：非微扰方法
Nonlinear normal modes in electrodynamic systems: A nonperturbative approach
摘要：
本文研究填充非线性非色散介质的圆柱谐振腔中的电磁非线性简正模。分析的主要特点是采用非线性场方程的精确解析解来详细研究模式特性。基于这种非微扰方法，我们严格地证明了在我们所考虑的一类分布保守系统中，自由非线性振动的总能量可以与系统的简正模能量之和精确地重合.这一事实意味着，能量正交性，这是迄今为止已知的只发生在线性振荡和领域，也可以观察到在非线性振荡系统。
英文摘要：
We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytical solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributive conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to take place only for linear oscillations and fields, can also be observed in the nonlinear oscillatory system.
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