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Yingjie Wang
2026-04-09 20:19:48 -04:00
parent c0b595d8d0
commit 729048ff55
1 changed files with 4 additions and 20 deletions
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@@ -267,26 +267,10 @@
\end{equation} \end{equation}
write $u^I = (\phi, \pi, \tensor{\psi}{_1}, \tensor{\psi}{_2}, \tensor{\psi}{_3})$, then the system can be written in the form of~\eqref{first-order-PDE} with write $u^I = (\phi, \pi, \tensor{\psi}{_1}, \tensor{\psi}{_2}, \tensor{\psi}{_3})$, then the system can be written in the form of~\eqref{first-order-PDE} with
\begin{equation} \begin{equation}
\tensor{A}{^1^I_J} = \begin{pmatrix} \tensor{A}{^i^I_J} = \begin{pmatrix}
0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\ 0 & 0 & -\tensor{e}{_i} \\
0 & -1 & 0 & 0 & 0 \\ 0 & -\tensor{e}{^i} & 0
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0
\end{pmatrix} \qc
\tensor{A}{^2^I_J} = \begin{pmatrix}
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0
\end{pmatrix} \qc
\tensor{A}{^3^I_J} = \begin{pmatrix}
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -1 \\
0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 0
\end{pmatrix} \qc \end{pmatrix} \qc
S=0. S=0.
\end{equation} \end{equation}