= Slowly varying triangular-jet envelope
{title2=$B\propto a^{-q/(1-2q)},\quad q=(1-\sqrt{1-4\Omega})/2$}
For $A_t=-a(\epsilon x)A_x-ia(\epsilon x)^2A_{xx}$, a downstream <WKB approximation> at fixed frequency $\Omega<1/4$ has local <wavenumber> $k=q/a$. The next-order <amplitude> equation is $(a-2a^2k)B_X=a^2k_XB$, giving the stated envelope. For small $\Omega$, it reduces to $B\propto a^{-\Omega}$ to first order in frequency. The approximation requires positive slowly varying width and separation from the double root at $\Omega=1/4$.
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