标题： 孤子气体基本势的高效计算 显示英文标题

标题： Efficient computation of soliton gas primitive potentials

摘要： 我们考虑计算一类孤子气体基本势的问题，这些势来自于物理域中无限区间上孤子的累积，扩展到$-\infty$。这种累积导致在若干个不相交的区间上产生一个相关的黎曼-希尔伯特问题。在跳跃矩阵具有特定平方根行为的情况下，我们描述了一种高效且准确的数值方法来解决这个黎曼-希尔伯特问题并提取势。该方法的关键首先是对黎曼-希尔伯特问题进行变形，并利用所谓的$g$函数进行数值计算；其次，将端点奇异性纳入所选基底以离散化和求解相关的奇异积分方程。 显示英文摘要

摘要： We consider the problem of computing a class of soliton gas primitive potentials for the Korteweg--de Vries equation that arise from the accumulation of solitons on an infinite interval in the physical domain, extending to $-\infty$. This accumulation results in an associated Riemann--Hilbert problem on a number of disjoint intervals. In the case where the jump matrices have specific square-root behavior, we describe an efficient and accurate numerical method to solve this Riemann--Hilbert problem and extract the potential. The keys to the method are, first, the deformation of the Riemann--Hilbert problem, making numerical use of the so-called $g$-function, and, second, the incorporation of endpoint singularities into the chosen basis to discretize and solve the associated singular integral equation.