= Anisotropic transverse scaling of an isotropic roll envelope
{title2=$X=\varepsilon x,\quad Y=\varepsilon^{1/2}y,\quad T=\varepsilon^2t$}
At a nonzero critical <wavenumber> in an isotropic medium, a small transverse wavevector changes its magnitude only at second order. Balancing radial detuning therefore requires the displayed unequal slow-space scales. With the positive carrier $e^{ik_cx}$, the leading <Newell–Whitehead–Segel equation> spatial term is $\xi(\partial_X-i\partial_Y^2/(2k_c))^2A$. A roll detuning $q$ has transverse phase growth $-\xi qp^2/k_c-\xi p^4/(4k_c^2)$; negative $q$ permits a <zigzag instability>. Changing the carrier convention changes the accompanying sign of $q$. Replacing this operator by an isotropic second-order Laplacian misses the critical circle's geometry.
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