论文标题
第四次Parelevé方程的Clarkson-McLeod解决方案的单数渐近学
Singular asymptotics for the Clarkson-McLeod solutions of the fourth Painlevé equation
论文作者
论文摘要
我们考虑了第四个Painlevé方程的Clarkson-clar-clar-cleod解决方案。这个解决方案家族的行为就像$κD_{α-\ frac {1} {2}}}^2（\ sqrt {2} x）$作为$ x \ rightarrow +\ rightarrow +\ infty $，$κ$，其中$κ$是任意的真实常数和$ d_ {α-{α-\ freac iS} $ par par par par and par par and par and cy}使用Deift-Zhou非线性最陡的下降方法，当$ x \ to- \ to- \ infty $左右（$κ\ weft（κ-κ^*\ right）> 0 $时，我们将解决方案的奇异渐近学获取为$ x \ to- \ infty $。还明确评估了连接公式。这证明并扩展了克拉克森和麦克劳德的猜想，即当参数$κ>κ^*> 0 $时，克拉克森 - clarks-cle-clod solutions在负实际轴上具有无限的许多简单极点。
We consider the Clarkson-McLeod solutions of the fourth Painlevé equation. This family of solutions behave like $κD_{α-\frac{1}{2}}^2(\sqrt{2}x)$ as $x\rightarrow +\infty$, where $κ$ is an arbitrary real constant and $D_{α-\frac{1}{2}}(x)$ is the parabolic cylinder function. Using the Deift-Zhou nonlinear steepest descent method, we obtain the singular asymptotics of the solutions as $x\to-\infty$ when $κ\left( κ-κ^*\right )>0$ for some real constant $κ^*$. The connection formulas are also explicitly evaluated. This proves and extends Clarkson and McLeod's conjecture that when the parameter $κ>κ^*>0$, the Clarkson-McLeod solutions have infinitely many simple poles on the negative real axis.
