= Convection amplitude coupled to a conserved field
A representative scaled amplitude model has complex $A$ and real $B$ with
$$
A_T=A+A_{XX}-A|A|^2-AB,\qquad B_T=\sigma B_{XX}+\mu(|A|^2)_{XX},\qquad\sigma>0.
$$
<Periodic boundary conditions> conserve $\int B\,dX$, because the right-hand side is a total second derivative. The slow field can change long-wave <convection roll> stability and permit localized pulses. For zero mean $B$, the uniform <convection rolls> are $A=Re^{iqX}$, $R^2=1-q^2$, $B=0$.
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