Coupled Klein-Gordon equations and energy exchange in two-component systems
Coupled Klein-Gordon equations and energy exchange in two-component systems
复制标题
双组分系统中的耦合克莱因-戈登方程和能量交换
DOI：
10.1140/epjst/e2007-00202-0
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Khusnutdinova K
中科院分区：
文献类型：
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作者：
Khusnutdinova K
提出了一个耦合Klein-Gordon方程组作为双组分介质中一维非线性波动过程的模型（例如，弹性双层中的长纵波，其中非线性仅来自粘合材料）。我们讨论的模型（李群分类，守恒律，不变的解决方案）和特殊的解决方案表现出系统的两个物理组件之间的能量交换的一般性质。为了研究后者，我们考虑了弱非线性多相波列的动力学框架内的两对反向传播的波在两个耦合的Sine-Gordon方程组，并获得了一个渐近精确的描述波的振幅的耦合演化方程。然后我们讨论了这些弱非线性解的调制不稳定性及其对能量交换的影响。
A system of coupled Klein–Gordon equations is proposed as a model for one-dimensional nonlinear wave processes in two-component media (e.g., long longitudinal waves in elastic bi-layers, where nonlinearity comes only from the bonding material). We discuss general properties of the model (Lie group classification, conservation laws, invariant solutions) and special solutions exhibiting an energy exchange between the two physical components of the system. To study the latter, we consider the dynamics of weakly nonlinear multi-phase wavetrains within the framework of two pairs of counter-propagating waves in a system of two coupled Sine–Gordon equations, and obtain a hierarchy of asymptotically exact coupled evolution equations describing the amplitudes of the waves. We then discuss modulational instability of these weakly nonlinear solutions and its effect on the energy exchange.