Explicit correspondences between gradient trees in $\mathbb{R}$ and holomorphic disks in $T^{\ast }\mathbb{R}$

Fukaya and Oh studied the correspondence between pseudoholomorphic disks in $T^{\ast }M$ which are bounded by Lagrangian sections $\{L_i^{\epsilon }\}$ and gradient trees in $M$ which consist of gradient curves of $\{f_i-f_j\}$. Here, $L_i^{\epsilon }$ is defined by $L_i^{\epsilon }=$,graph$(\epsilon d{f}_i)$. They constructed approximate pseudoholomorphic disks in the case $\epsilon >0$ is sufficiently small. When $M=\mathbb{R}$ and Lagrangian sections are affine, pseudoholomorphic disks $w_{\epsilon }$ can be constructed explicitly. In this paper, we show that pseudoholomorphic disks $w_{\epsilon }$ converges to the gradient tree in the limit $\epsilon \to +0$ when the number of Lagrangian sections is three and four.