Theorem: NWS amplitude equation A_T = A - |A|^2 A has unique positive steady state A_s = 1

Theorem (NWS amplitude-saturation canonical): the dimensionless Newell-Whitehead-Segel amplitude equation A_T = A - |A|^2 A admits three real homogeneous fixed points: A = 0 (trivial, unstable for r > 0), A = +1 and A = -1 (saturated,…