We consider the numerical computation of finite-genus solutions of the Korteweg-de Vries equation when the genus is large. Our method applies both to the initial-value problem when spectral data can be computed and to dressing scenarios when spectral data is specified arbitrarily. In order to compute large genus solutions, we employ a weighted Chebyshev basis to solve an associated singular integral equation. We also extend previous work to compute period matrices and the Abel map when the genus is large, maintaining numerical stability. We demonstrate our method on four different classes of solutions. Specifically, we demonstrate dispersive quantization for "box" initial data and demonstrate how a large genus limit can be taken to produce a new class of potentials.

翻译：我们考虑Korteweg-de Vries 等方程式的有限基因溶液的计算方法。 我们的方法既适用于可计算光谱数据时的初始值问题,也适用于任意指定光谱数据时的组合情景。 为了计算大型基因溶液, 我们使用一个加权的Chebyshev 基础来解决一个相关的单元整体等式。 我们还将先前的工作扩大到计算时段矩阵和Abel 地图, 以保持数字稳定性。 我们用四种不同的溶液来演示我们的方法。 具体地说, 我们展示了“ 箱” 初步数据的分散量化, 并演示了如何使用大基因极限来产生新的潜力类别 。