Analytical Solution for the two-dimensional wave equation, separation of variables
Since the lhs and rhs are again independent of each other, we can separate the latter equation into two independent
equations, one for
x and one for
y , namely
\begin{equation*}
H_{xx} + \kappa^2H = 0,
\end{equation*}
and
\begin{equation*}
Q_{yy} + \rho^2Q = 0,
\end{equation*}
with
\rho^2= \nu^2-\kappa^2 .