We propose a numerical algorithm that computes the eigenvalues of the Korteweg–de Vries equation (KdV) from sampled input data with vanishing boundary conditions. It can be used as part of the Non-linear Fourier Transform (NFT) for the KdV equation. The algorithm that we propose makes use of Sturm Liouville (SL) oscillation theory to guaranty that all eigenvalues are found. In comparison to similar available algorithms, we show that our algorithm is more robust to numerical errors and thus more reliable. Furthermore we show that our root finding algorithm, which is based on the Newton–Raphson (NR) algorithm, typically saves computation time compared to the conventional approaches that rely heavily on bisection.

我们提出了一种数值算法，该算法从边界条件消失的采样输入数据中计算 Korteweg-de Vries 方程 (KdV) 的特征值。它可以用作 KdV 方程的非线性傅立叶变换 (NFT) 的一部分。我们提出的算法利用 Sturm Liouville (SL) 振荡理论来保证找到所有特征值。与类似的可用算法相比，我们表明我们的算法对数值误差更稳健，因此更可靠。此外，我们展示了我们的寻根算法，它基于 Newton-Raphson (NR) 算法，与严重依赖二分法的传统方法相比，通常可以节省计算时间。