 Newell–Whitehead–Segel equation

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 $q{k}^2-k^4/4$, 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.