A propagating chemical front can persist when only one species diffuses. For ut=u(1−u−βv)+uxx, vt=−δuv, set z=x−ct, k2=1−δ/2, c=−δ/(2k) and βv0=2−δ, with 0<δ<2. The displayed profiles satisfy both equations because U′=kU(1−U) and V′/V=−2kU. They connect (u,v)=(0,v0) to (1,0): the second concentration changes by local reaction, even without its own diffusion.
