Painlevé-III Monodromy Maps Under the $D_6\to D_8$ Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions

Ahmad Barhoumi, Oleg Lisovyy, Peter D. Miller +1

The third Painlevé equation in its generic form, often referred to as Painlevé-III($D_6$), is given by $$ \frac{{\rm d}^2u}{{\rm d}x^2} =\frac{1}{u}\left(\frac{{\rm d}u}{{\rm d}x}\…