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\end{theorem}
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\end{frame}
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\begin{frame}{Searching for a first order Z4c}{First order reduction}
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\begin{frame}{First order reduction: wave equation as an example}
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\subsection{First order reduction: wave equation as an example}
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We can introduce auxiliary variables to reduce a second order PDE system to a first order one. For example, for the wave equation on flat spacetime:
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\begin{equation}
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