论文标题
Korteweg-De Vries方程的大型溶液的计算
Computation of Large-Genus Solutions of the Korteweg-de Vries Equation
论文作者
论文摘要
当属较大时，我们考虑了Korteweg-De Vries方程的有限基因溶液的数值计算。当可以计算光谱数据时，我们的方法都适用于初始值问题，并且在任意指定光谱数据时对场景进行打扮。为了计算大型属溶液，我们使用加权的Chebyshev基础来求解相关的单数积分方程。我们还将以前的工作扩展到计算周期矩阵和属属时的亚abel图，并保持数值稳定性。我们在四种不同类别的解决方案上演示了我们的方法。具体而言，我们证明了“盒子”初始数据的分散量化，并证明了如何采用大属极限来产生一类新的电位。
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.
