论文标题
一般的不变扩散过程
A general class of invariant diffusion processes in one dimension
论文作者
论文摘要
本文改进了先前建立的测试，该测试仅涉及系数，以确定是否存在大型时空依赖性扩散过程的非平地对称性是否存在。当确保这些对称性的存在的存在时，向规范形式的转换允许四维或六维对称组，并且它们的无限发电机的完整列表即可立即处置，而当至少一个系数是任意选择时，就没有任何麻烦的计算。我们以深度对称性和降低性能以及在应用中产生的六个模型的物理重要解决方案进行研究。
This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on the real line exist. When the existence of these symmetries are ensured, the transformation to canonical forms admitting either four- or six-dimensional symmetry groups and the full list of their infinitesimal generators are then immediately at our disposal without any cumbersome calculations that happen when at least one of the coefficients is arbitrarily chosen. We study in depth symmetry and reducibility properties and physically important solutions of six models arising in applications.
