From 498b7104929de4b19218a6d707467cf2a40be304 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 20:09:29 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/report.tex b/report.tex
index cf2fcff..cf45df9 100644
--- a/report.tex
+++ b/report.tex
@@ -261,8 +261,8 @@
     \begin{equation}
       \begin{cases}
         \Partial{t}{\phi} = \pi, \\
-        \pdvt{\psi} = \pdv{\pi}{x}, \\
-        \pdvt{\pi} = \pdv{\psi}{x}.
+        \Partial{t}{\tensor{\psi}{_i}} = \pdv{\pi}{x}, \\
+        \Partial{t}{\pi} = \pdv{\tensor{\psi}{_i}}{x}.
       \end{cases}
     \end{equation}
     write $u^I = (\phi, \pi, \psi)$, then the system can be written in the form of~\eqref{first-order-PDE} with