\begin{equation*}
\fontsize{12.0}{12.0}\selectfont
   c_{gx} \equiv \DP{\omega}{k} 
                   = \frac{\beta (k^2-l^2)}{(k^2+l^2)^2},
  \quad
   c_{gy} \equiv \DP{\omega}{l} 
                   = \frac{2 \beta k l}{(k^2+l^2)^2}.
\end{equation*}
