  We show that, when compactified on a circle, N=(2,0),d=6 supergravity coupled
to 1 tensor multiplet and nV vector multiplets is dual to N=(2,0),d=6
supergravity coupled to just nT=nV+1 tensor multiplets and no vector
multiplets. Both theories reduce to the same models of N=2,d=5 supergravity
coupled to nV5=nV+2 vector fields. We derive Buscher rules that relate
solutions of these theories (and of the theory that one obtains by dualizing
the 3-form field strength) admitting an isometry. Since the relations between
the fields of N=2,d=5 supergravity and those of the 6-dimensional theories are
the same with or without gaugings, we construct supersymmetric non-Abelian
solutions of the 6-dimensional gauged theories by uplifting the recently found
5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions
describe the usual superpositions of strings and waves supplemented by a BPST
instanton in the transverse directions. One of the solutions obtained
interpolates smoothly between two AdS3xS3 geometries with different radii.
