不同类型模式间的相互作用引起哈密顿系统的共振扰动

本文讨论了两种不同类型的模式耦合的一个哈密顿系统。在无耦合时,其中一类模式是描写相干三波相互作用的非线性振子,组成可积的哈密顿量。另一类模式是不变量。在耦合的一级近似下,我们证明了耦合将在相空间中引入共振区,共振条件与振子固有的线性频率、频率失谐以及振子振幅的非线性变化的谐波频率有关。 关键词：

RESONANCE PERTURBATION OF A HAMILTONIAN BY COUPLING OF TWO DIBBERENT KINDS OF MODES

A Hamiltonian system with coupled two dibberent kinds of modes is studied. When the coupling vanishes, one kind of modes is nonlinear oscillators, describing coherent three-wave interaction and consisting an integrable Hamiltonian. Another kind of modes is constants of motion. In the first order of approximation, resonance occurs due to the coupling between these two kinds of modes. The resonace condition is relevant to the existing linear brequencies and their mismatch as well as the harmonic frequencies of the nonlinear variations of the amplitudes of the oscillators.