5 citations · 8 across the 6 of their papers we have counts for
7 papers
Asymptotics and total integrals of the tritronquée solution and its Hamiltonian
Dan Dai, Wen-Gao Long
We study the tritronquée solution of the equation, the second member of the Painlevé I hierarchy. This solution is pole-free on the real line and…
Connection problem of the first Painlevé transcendents with large initial data
Wen-Gao Long, Yu-Tian Li
In previous work, Bender and Komijani (2015 \textit{J. Phys. A: Math. Theor.} 48, 475202) studied the first Painlevé (PI) equation and showed that the sequence of initial condition…
Connection problem of the first Painlevé transcendent between poles and negative infinity
Wen-Gao Long, Yu-Tian Li, Qing-hai Wang
We consider a connection problem of the first Painlevé equation (), trying to connect the local behavior (Laurent series) near poles and the asymptotic behavior as th…
On the connection problem for the second Painlevé equation with large initial data
Wen-Gao Long, Zhao-Yun Zeng
We consider two special cases of the connection problem for the second Painlevé equation (PII) using the method of uniform asymptotics proposed by Bassom et al.. We give a classifi…
Real solutions of the first Painlevé equation with large initial data
Wen-Gao Long, Yu-Tian Li, Sai-Yu Liu +1
We consider three special cases of the initial value problem of the first Painlevé equation (PI). Our approach is based on the method of uniform asymptotics introduced by Bassom, C…
A note on the connection problem of some special Painlevé V functions
Wen-Gao Long, Zhao-Yun Zeng, Jian-Rong Zhou
As a new application of the method of "uniform asymptotics" proposed by Bassom, Clarkson, Law and McLeod, we provide a simpler and more rigorous proof of the connection formulas of…
Proof of a conjecture of Granath on optimal bounds of the Landau constants
Chun-Ru Zhao, Wen-Gao Long, Yu-Qiu Zhao
We study the asymptotic expansion for the Landau constants , \begin{equation*} πG_{n}\sim \ln(16N)+γ+\sum^{\infty}_{k=1}\frac{α_k}{N^k} ~~\mbox{as} ~ n\rightarrow\infty, \end{…