  We consider polarons in models of coupled electronic and vibrational degrees
of freedom, in the presence of a soft nonlinear inter-particle potential (Morse
potential). In particular, we focus on a a bound state of a polaron with a
breather, a so-called ``polarobreather''. We analyze the existence of this
branch based on frequency resonance conditions and illustrate its stability
using Floquet spectrum techniques. Multi-site solutions of this type are also
obtained both in the stationary case (two-site polarons) and in the breathing
case (two-site polarobreathers). We also obtain a different branch of
solutions, namely a polaronic nanopteron.

Soft Condensed Matter;Pattern Formation and Solitons