Traveling phase waves are commonly observed in recordings of the cerebral cortex and are believed to organize behavior across different areas of the brain. We use this as motivation to analyze a one-dimensional network of phase oscillators that are nonlocally coupled via the phase response curve (PRC) and the Dirac delta function. Existence of waves is proven and the dispersion relation is computed. Using the theory of distributions enables us to write and solve an associated stability problem. First and second order perturbation theory is applied to get analytic insight and we show that long waves are stable while short waves are unstable. We apply the results to PRCs that come from mitral neurons. We extend the results to smooth pulse-like coupling by reducing the nonlocal equation to a local one and solving the associated boundary value problem.

行相波通常在大脑皮层的记录中观察到，并且被认为可以组织大脑不同区域的行为。我们以此为动机来分析通过相位响应曲线 (PRC) 和 Dirac delta 函数非局部耦合的相位振荡器的一维网络。证明了波的存在并计算了色散关系。使用分布理论使我们能够编写和解决相关的稳定性问题。应用一阶和二阶微扰理论来获得分析洞察力，我们表明长波是稳定的，而短波是不稳定的。我们将结果应用于来自二尖瓣神经元的 PRC。我们通过将非局部方程简化为局部方程并求解相关的边界值问题，将结果扩展到平滑脉冲状耦合。