论文标题
在扰动的第二个painlevé方程式上
On the Perturbed Second Painlevé Equation
论文作者
论文摘要
我们考虑第二个Painlevé方程式的扰动版本（$ \ textrm {p} _ {\ textrm {ii}} $），该版本在应用中出现，并表明它具有类似于著名的Hastings Hastings-Mcleod和Tritronquhe and tritronquh and tritronquh and $ \ textrm {pextrm {pextrm {p} $ {$ {$ {扰动方程的Hastings-clood型溶液在整个现实线上是全体形态的，实用值和正面的，而Tritronquée-Type溶液在复杂平面的大型扇区中是全态。这些属性还表征了$ \ textrm {p} _ {\ textrm {ii}} $的相应解决方案，并且令人惊讶，因为扰动的方程没有其他特征在于$ \ textrm {p} _ {\ textrm {\ textrm {ii}} $，尤其是Painlevel的$ \ textrm {p} _ {p} _ {p} _ {p}。
We consider a perturbed version of the second Painlevé equation ($\textrm{P}_{\textrm{II}}$), which arises in applications, and show that it possesses solutions analogous to the celebrated Hastings-McLeod and tritronquée solutions of $\textrm{P}_{\textrm{II}}$. The Hastings-McLeod-type solution of the perturbed equation is holomorphic, real-valued and positive on the whole real-line, while the tritronquée-type solution is holomorphic in a large sector of the complex plane. These properties also characterise the corresponding solutions of $\textrm{P}_{\textrm{II}}$ and are surprising because the perturbed equation does not possess additional distinctive properties that characterise $\textrm{P}_{\textrm{II}}$, particularly the Painlevé property.
