大质量Thirring模型中驻定周期波的稳定性
Stability of standing periodic waves in the massive Thirring model
AI总结：
本文通过Lax谱方法结合解析与数值分析，证明大质量Thirring模型中驻定周期波的谱稳定性等价于其八个端点本征值位于虚轴或复平面对角线上。
摘要：
我们在实验室坐标下分析大质量Thirring模型（MTM）中驻定周期波的谱稳定性。由于线性化MTM方程的解与线性Lax系统的平方本征函数相关，驻定周期波的谱稳定性可以通过其Lax谱来研究。驻定周期波根据八个本征值进行分类，这些本征值与Lax谱的谱带端点重合。结合解析方法和数值方法，我们证明驻定周期波是谱稳定的，当且仅当这八个本征值位于虚轴上或复平面的对角线上。
英文摘要：
We analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability of the standing periodic waves can be studied by using their Lax spectrum. Standing periodic waves are classified based on eight eigenvalues which coincide with the endpoints of the spectral bands of the Lax spectrum. Combining analytical and numerical methods, we show that the standing periodic waves are spectrally stable if and only if the eight eigenvalues are located either on the imaginary axis or along the diagonals of the complex plane.
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