= False complex saddle in dissipative cubic dispersion
{title2=$\alpha=-1,\quad\beta=1,\quad\gamma=1/10$}
For these constants, every real-wavenumber <growth rate> is $-k^2-1/10<0$. The real-contour impulse integral decays with envelope $e^{-t/10}t^{-1/2}$ at fixed position. Yet the stationary candidate $k=-2i/3$ has $\operatorname{Im}\omega=4/27-1/10>0$. It cannot be a contributing <spatial pinch point>; otherwise it would contradict the real-contour growth bound. This explicit example shows why solving the algebraic saddle equations is insufficient for <absolute wave-packet instability>.
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