In previous works, it was shown that the propagation of magnetic spin waves in thin films can be approximated by a nonlinear Schrödinger-type equation. The formulation begins with the magnetostatic equations (Gauss and Ampere’s laws of magnetism) and the Landau–Lifshitz equation. The solution of this system is a potential function whose dimensionless amplitude is the solution of a nonlinear Schrödinger. In the current work, we are demonstrating an efficient infinite series solution using the Christov functions. This is the first time the functions are used in problems involving complex arithmetics. The solutions of the time-independent and time-dependent problems are given in complex series form.

中文翻译：

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一种高效且高精度的光谱方法，用于建模薄膜中孤磁自旋波的传播

在以前的工作中，已经表明，可以通过非线性Schrödinger型方程来近似薄膜中的磁性自旋波的传播。该公式从静磁方程（高斯和安培磁定律）和Landau–Lifshitz方程开始。该系统的解是一个势函数，其无量纲振幅是非线性薛定ding的解。在当前的工作中，我们正在演示使用Christov函数的高效无限级数解。这是函数首次用于涉及复杂算术的问题中。与时间无关和与时间有关的问题的解决方案以复杂的级数形式给出。