论文标题
线性化的正弦 - 戈登方程的准周期溶液的新Evans函数
A new Evans function for quasi-periodic solutions of the linearised sine-Gordon equation
论文作者
论文摘要
我们构建了一个新的Evans函数，用于准周期溶液，以实现有关周期性行驶波的正弦方程的线性化。这种埃文斯功能是根据山丘方程的基本解决方案编写的。将Evans-Krein函数理论应用于我们的Evans函数，我们提供了一种新方法，用于计算线性化的正弦戈登方程的简单特征值的角质签名。通过更改floquet指数参数为准周期溶液参数，我们计算正弦 - 戈登方程的周期性波动波解决方案的线性化光谱，并通过角质签名轨迹轨迹。最后，我们表明，我们的新Evans函数可以很容易地应用于具有非周期势能的非线性klein-gordon方程的一般情况。
We construct a new Evans function for quasi-periodic solutions to the linearisation of the sine-Gordon equation about a periodic travelling wave. This Evans function is written in terms of fundamental solutions to a Hill's equation. Applying Evans-Krein function theory to our Evans function, we provide a new method for computing the Krein signatures of simple characteristic values of the linearised sine-Gordon equation. By varying the Floquet exponent parametrising the quasi-periodic solutions, we compute the linearised spectra of periodic travelling wave solutions of the sine-Gordon equation and and track dynamical Hamiltonian-Hopf bifurcations via the Krein signature. Finally, we show that our new Evans function can be readily applied to the general case of the nonlinear Klein-Gordon equation with a non-periodic potential.
