论文标题
某些椭圆山潜力的特性
Properties of some elliptic Hill's potentials
论文作者
论文摘要
我们研究了Hill的微分方程，并通过椭圆函数表达的电势，这在某些物理和数学问题中产生。分析方法可以应用于参数空间的渐近区域中电势的局部特性。确定电势点的位置，当它们接近鞍点时，也可以确定转弯点的位置。这些局部数据与与差分方程相关的二次差异结合，为最近获得的渐近征出征收提供了定性解释。一个相关的主题是关于具有双周期椭圆函数系数的ode floquet定理的概括，该系数具有一些新功能，与具有真实有价值的单个周期系数的ODE相比。除了局部渐近区域外，还使用数值方法研究了椭圆势的全局特性。
We study Hill's differential equation with potential expressed by elliptic functions which arises in some problems of physics and mathematics. Analytical method can be applied to study the local properties of the potential in asymptotic regions of the parameter space. The locations of the saddle points of the potential are determined, the locations of turning points can be determined too when they are close to a saddle point. Combined with the quadratic differential associated with the differential equation, these local data give a qualitative explanation for the asymptotic eigensolutions obtained recently. A relevant topic is about the generalisation of Floquet theorem for ODE with doubly-periodic elliptic function coefficient which bears some new features compared to the case of ODE with real valued singly-periodic coefficient. Beyond the local asymptotic regions, global properties of the elliptic potential are studied using numerical method.
