Travelling-frame formulation for radial invasion fronts in half-line amplitude equations

Ascertain whether a travelling-wave change of variables can be formulated for the radial Ginzburg–Landau-type amplitude equations derived on the half-line R ≥ 0 with the compatibility condition ∂R A(0) = 0, so as to describe radial invasion fronts analogous to invading one-dimensional fronts.

Background

The amplitude equations obtained in the paper are radial and posed on the half-line due to the use of polar coordinates, with a Neumann-type compatibility condition at the origin. The authors point out the interest in radial invasion fronts—circular fronts where patterned regions invade the uniform state—but note that the half-line geometry complicates the usual travelling-frame approach familiar from one-dimensional front theory.

This raises an explicit methodological question about whether a travelling-frame formulation is compatible with the boundary condition at R = 0, and whether such a formulation can capture radial invasion dynamics within the derived amplitude-equation framework.