On the stability of the compacton waves for the degenerate KdV and NLS models

In this paper, we consider the degenerate semi-linear Schrödinger and Korteweg-de Vries equations in one spatial dimension. We construct special solutions of two models, namely standing wave NLS traveling waves, which turn out to have compact support, compactons. show that compactons are unique bell-shaped corresponding PDEs for appropriate variational problems as well. provide a complete spectral characterization such all values p p . Namely, waves spectrally stable alttext="2 greater-than p less-than-or-equal-to 8"> 2 > ≤ 8 encoding="application/x-tex">2>p\leq 8 , while single mode instability occurs alttext="p encoding="application/x-tex">p>8 This extends previous work Germain, Harrop-Griffiths Marzuola [Quart. Appl. Math. 78 (2020), pp. 1–32] who previously established orbital stability some specific range