  A couple of applications of B\"acklund transformations in the study of
nonlinear evolution equations is here given. Specifically, we are concerned
about third order nonlinear evolution equations. Our attention is focussed on
one side, on proving a new invariance admitted by a third order nonlinear
evolution equation and, on the other one, on the construction of solutions.
Indeed, via B\"acklund transformations, a {\it B\"acklund chart}, connecting
Abelian as well as non Abelian equations can be constructed. The importance of
such a net of links is twofold since it indicates invariances as well as allows
to construct solutions admitted by the nonlinear evolution equations it
relates. The present study refers to third order nonlinear evolution equations
of KdV type. On the basis of the Abelian
  wide B\"acklund chart which connects various different third order nonlinear
evolution equations an
  invariance admitted by the {\it Korteweg-deVries interacting soliton}
(int.sol.KdV) equation is obtained and a related new explicit solution is
constructed.
  Then, the corresponding non-Abelian {\it B\"acklund chart}, shows how to
  construct matrix solutions of the mKdV equations: some recently obtained
solutions are reconsidered.
