标题： 一种$P$-自适应Hermite方法用于非线性色散麦克斯韦方程 显示英文标题

标题： A $P$-Adaptive Hermite Method for Nonlinear Dispersive Maxwell's Equations

摘要： 在本工作中，我们引入了一种新颖的埃尔米特方法来处理非线性色散介质中的麦克斯韦方程。 该方法实现了高阶精度，并且不需要任何非线性代数求解器，而是需要求解小的局部线性系统，其维度与阶数无关。 在此设置下，顺序自适应算法的实现非常直接，使得得到的p自适应埃尔米特方法适用于孤子样波传播的模拟。 显示英文摘要

摘要： In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small local linear systems for which the dimension is independent of the order. The implementation of order adaptive algorithms is straightforward in this setting, making the resulting p-adaptive Hermite method appealing for the simulations of soliton-like wave propagation.