论文标题
向非线性波方程的行驶波解决方案的稳定性和不稳定性
Stability and instability of traveling wave solutions to nonlinear wave equations
论文作者
论文摘要
在本文中，我们研究了平面波溶液对满足无效条件的波方程半线性系统的稳定性和不稳定性。我们确定了一个条件，该条件使我们能够证明平面波的全局非线性渐近稳定性。全局稳定性的证明要求我们分析背景波浪和扰动之间相互作用的几何形状。当未满足这种情况时，我们能够证明假设有额外的通用条件，就可以证明线性不稳定性。使用几何光学元素ANSATZ显示线性不稳定性。
In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition which allows us to prove the global nonlinear asymptotic stability of the plane wave. The proof of global stability requires us to analyze the geometry of the interaction between the background plane wave and the perturbation. When this condition is not met, we are able to prove linear instability assuming an additional genericity condition. The linear instability is shown using a geometric optics ansatz.
