Selection of modulated pushed pattern-forming fronts

Let $u_\mathrm{ps}(\xi,\tau)$ be a modulated pushed pattern-forming front, namely a temporally modulated pushed front leaving a pattern-forming wake. Selection of modulated pushed pattern-forming fronts. $u_\mathrm{ps}(\xi,\tau)$ should be a selected front.

The source expects this result to follow by transferring the available linearized-dynamics analysis for rigid pattern-forming fronts to the modulated setting; the conjecture is not established there.