Numerical Continuation and Bifurcation in Nonlinear PDEs: Stability, invasion and wavetrains in the Swift-Hohenberg equation

The paper states the linear-spreading-speed characterization via pinched double roots and records the consequences λ*(c*) = iω* with ω*>0 and Re ν*(c*)<0, plus the 1:1 resonance (node conservation) k* = ω*/c* for Swift–Hohenberg pulled fronts, aligning with the candidate solution’s conclusions. The model provides an explicit implicit-function-theorem calculation, deriving dλ*/dc = ν* and showing the transverse crossing of Re λ* through zero at c=c*, which the paper does not detail but is consistent with its statements. See the paper’s definitions of dc(λ,ν) (its equation (20)), the double-root condition (21), the speed characterization (22), and the explicit statement of ω* = c* k* via node conservation for fronts in §5 .