  We consider a one dimensional model of an electron in a doubly (or nearly)
degenerate band that interacts with elastic distortions. We show that the
electron equations of motion reduce to a set of coupled non-linear Schrodinger
equations. For the case of interband electron-phonon coupling stemming from
local Jahn-Teller interactions, new multicomponent self-localized polaron
solutions --vector polarons-- are described and classified. The phase diagram
for the different types of vector polarons in this model is presented. By
interpreting the components of the orbital doublet as those of spin-1/2, our
results can also be used to describe bound magnetic polarons.
