= Two boundary traces for reverse-dispersion Airy flow
{title2=$\widetilde g_2=Q_0(-ir)-r\widetilde g_1-r^2\widetilde g_0,\quad r^3=p$}
For $q_t-q_{xxx}=0$ on $x>0$, evaluate the <global relation> at $k=-ir/2$, where $\operatorname{Re}p>0$ and the principal cube root $r=p^{1/3}$ has positive real part. The time exponent becomes $-p$, giving the displayed <Laplace transform> identity. Thus the second-derivative trace is determined once the value and first-derivative traces are prescribed. The homogeneous transformed equation $u'''-pu=0$ has exactly two spatially decaying roots, so two independent admissible conditions are required. One condition leaves a free decaying mode; three independent conditions generally violate the global constraint.
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