= Weak wave cascade
{title2=$\tau_{\mathrm{cas}}\sim\tau_{\mathrm{nl}}^2/\tau_w$}
If a wave packet experiences a fractional nonlinear change $\chi=\tau_w/\tau_{\mathrm{nl}}\ll1$ per interaction, and successive interaction phases are decorrelated, $N$ changes add as a <random walk> of size $\sqrt N\chi$. Order-one transfer needs $N\sim\chi^{-2}$ interactions, giving the displayed cascade time. Phase coherence or resonant constraints can alter this estimate; weakness alone does not justify random addition.
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