A Renormalization Method for Modulational Stability of Quasi-Steady Patterns in Dispersive Systems
A Renormalization Method for Modulational Stability of Quasi-Steady Patterns in Dispersive Systems
复制标题
色散系统中准稳态模式调制稳定性的重正化方法
DOI：
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发表时间：
2002
影响因子：
2
通讯作者：
K. Promislow
中科院分区：
文献类型：
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作者：
K. Promislow
我们采用全球准定常流形严格减少被迫，线性阻尼色散偏微分方程有限维流。我们考虑的流形不是不变的，但通过重整化群方法，我们捕获了整个系统的长期演化作为流形上的流。对于参数化的非线性薛定谔方程，我们考虑一个流形描述N个分离良好的脉冲，并推导出一个显式系统的常微分方程的流动的流形上捕获的领先的顺序脉冲运动通过的尾巴-尾巴的相互作用。我们还概述了严格的双曲PNLS和四阶抛物相敏放大方程的光纤系统的缓慢演变之间的联系。
We employ global quasi-steady manifolds to rigorously reduce forced, linearly damped dispersive partial differential equations to finite dimensional flows. The manifolds we consider are not invariant, but through a renormalization group method we capture the long-time evolution of the full system as a flow on the manifold. For the parametric nonlinear Schrodinger equation we consider a manifold describing N well-separated pulses and derive an explicit system of ordinary differential equations for the flow on the manifold which captures the leading order pulse motion through the tail-tail interactions. We also outline a rigorous connection between the slow evolution in the hyperbolic PNLS and the fourth-order parabolic phase sensitive amplification equation for fiber optic systems.