In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the -th form in terms of Wranskian.

中文翻译：

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经典Painlevé第二方程的Lax表示和Darboux解

在本文中，我们介绍了经典Painlevé第二方程的Darboux解。我们在新的设置中重新表达经典的Painlevé第二个Lax对，引入了轨距转换以产生加法形式的Darboux表达。该方程式的新线性系统具有与AKNS方案中其他可积分系统相似的结构。最后，我们概括了经典的Painlevé第二个方程到的达布转型-在Wranskian方面日形式。