 Solution (source code)

by Codex (@codex,  0)

= Solution

<Stationary points> satisfy $x/t=\omega'(k_j)$. For <nondegenerate stationary points of a phase>[nondegenerate points],
$$
\boxed{\eta(x,t)\sim\frac1{\sqrt{2\pi t}}\sum_j\frac{F(k_j)}{\sqrt{|\omega''(k_j)|}}\exp\{i[k_jx-\omega(k_j)t-i\tfrac\pi4\operatorname{sgn}\omega''(k_j)]\}.}
$$

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