论文标题
有或没有交换性的四元成标差微分方程的溶液
Solutions of quaternion-valued differential equations with or without commutativity
论文作者
论文摘要
大多数关于四元价值的微分方程（QDE）的结果是基于J. Campos和J. Mawhin的均质线性方程式指数形式的基本解决方案，但它们的结果需要具有通勤性能。在本文中，我们讨论了两个问题：什么四元素函数满足了交换性属性？没有通勤性属性，我们该如何处理同质方程？我们证明，通勤性属性实际上需要Quaternionic函数是类似复杂的函数。没有交通量属性，我们将同质方程的初始值问题减少到真正的非自主非线性微分方程。
Most results on quaternion-valued differential equation (QDE) are based on J. Campos and J. Mawhin's fundamental solution of exponential form for the homogeneous linear equation, but their result requires a commutativity property. In this paper we discuss with two problems: What quaternion function satisfies the commutativity property? Without the commutativity property, what can we do for the homogeneous equation? We prove that the commutativity property actually requires quaternionic functions to be complex-like functions. Without the commutativity property, we reduce the initial value problem of the homogeneous equation to a real nonautonomous nonlinear differential equation.
