Tokman Mikhail, Erukhimova Maria
Institute of Applied Physics Russian Academy of Sciences, Nizhny Novgorod, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056610. doi: 10.1103/PhysRevE.84.056610. Epub 2011 Nov 23.
We study the system of equations for the canonically conjugate variables p and q specified by the one-dimensional Hamiltonian H=H(p,q,Λ(1),...,Λ(N)) dependent on Nself-consistent slightly changing parameters obeying the equations: Λ(n)=εf(n)(Λ(1),...,Λ(N),p,q). A broad range of oscillatory and wave processes with weak dissipation is described by analogous systems. The general method of adiabatic invariant construction for this system is proposed. Self-consistent averaged equations for the evolution of the action integral and the parameters Λ(n) are obtained. The constructed theory is applied to a generalized model of the nonlinear resonance. The autoresonance (phase locking) regime of decay parametric instability in a dissipative medium is revealed.
我们研究由一维哈密顿量(H = H(p,q,\Lambda^{(1)},\cdots,\Lambda^{(N)}))所确定的正则共轭变量(p)和(q)的方程组，该哈密顿量依赖于(N)个服从方程(\Lambda^{(n)}=\varepsilon f^{(n)}(\Lambda^{(1)},\cdots,\Lambda^{(N)},p,q))的自洽微变参数。类似的系统描述了具有弱耗散的广泛振荡和波动过程。提出了该系统绝热不变量构建的一般方法。得到了作用积分和参数(\Lambda^{(n)})演化的自洽平均方程。将构建的理论应用于非线性共振的广义模型。揭示了耗散介质中衰减参量不稳定性的自共振（锁相） regime 。
