Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2 N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6 .

中文翻译：

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mKdV 方程和多参数有理解

摘要 修正 Korteweg-de Vries (mKdV) 方程的 N 阶解由两个 N 阶 wronskian 的商给出，取决于 2 N 个实参数。当这些参数之一变为 0 时，我们成功地为每个正整数 N 获得作为 x 和 t 中多项式的商的有理解，这取决于 2 N 个实参数。我们为 N = 1 直到 N = 6 阶构建这些有理解的显式表达式。