Rational solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders $n=1$ until 10.

中文翻译：

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与特定多项式相关的 mKdV 方程的有理解

修正的 Korteweg-de Vries (mKdV) 方程的有理解是根据涉及某些特定多项式的行列式的商给出的。这提供了一种非常有效的方法来构建解决方案。我们很容易为一阶构造这些有理解的显式表达式$n=1$ 直到 10。