Subharmonic dynamics of wave trains in reaction–diffusion systems

We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically (with asymptotic phase) with exponential rates decay when subject $NT$-periodic, i.e., subharmonic, perturbations. However, both allowable size perturbations depend on $N$, and, particular, they tend zero as $N\to\infty$, leading a lack uniformity subharmonic results. In this work, we build recent work by authors introduce methodology that allows us achieve result for which is uniform $N$. Our motivated localized (i.e. integrable line), has recently received considerable attention many authors.