= Newell–Whitehead–Segel equation
{c}
{title2=$A_T=\mu A+(\partial_X+i\partial_Y^2/2)^2A-|A|^2A$}
The Newell–Whitehead–Segel equation is an <amplitude equation> for slowly modulated stationary rolls in an isotropic pattern-forming medium. With the displayed sign convention, a roll $A=R e^{iqX}$ has $R^2=\mu-q^2$. A transverse <phase modulation> has linear growth rate $qk^2-k^4/4$, so long-wave transverse instability occurs for $q>0$. Reversing the carrier-wave convention reverses the sign attached to its detuning $q$; one must derive the stability sign from the operator actually used.
Back to article page
