Coexistence fraction of a conserved-field amplitude mesa (source code)

= Coexistence fraction of a conserved-field amplitude mesa
{title2=$h=\frac{9(1-\delta)^2\mu}{4\delta\alpha^2}+\frac{1-\delta}{2\delta}$}

For $0<\delta<1$ and $\alpha\ne0$, a broad localized plateau in the <conserved-field real amplitude equation> has effective parameter $\nu=\mu-\delta\langle A^2\rangle$ and stationary equation $A''+\nu A+\alpha A^2-(1-\delta)A^3=0$. Equal endpoint values of its first integral give $R=2\alpha/[3(1-\delta)]$, $\nu=-2\alpha^2/[9(1-\delta)]$. If the plateau occupies fraction $h$ of a long periodic interval, $\langle A^2\rangle\simeq hR^2$ supplies the displayed relation. It applies when both the plateau and exterior are long relative to the front width; $0<h<1$ gives its leading existence interval.