  A systematic construction of a class of integrable hierarchy is discussed in
terms of the twisted affine $A_{2r}^{(2)}$ Lie algebra. The zero curvature
representation of the time evolution equations are shown to be classified
according to its algebraic structure and according to its vacuum solutions. It
is shown that a class of models admit both zero and constant (non zero) vacuum
solutions. Another, consists essentially of integral non-local equations and
can be classified into two sub-classes, one admitting zero vacuum and another
of constant, non zero vacuum solutions.
  The two dimensional gauge potentials in the vacuum plays a crucial ingredient
and are shown to be expanded in powers of the vacuum parameter $v_0$. Soliton
solutions are constructed from vertex operators, which for the non zero vacuum
solutions, correspond to deformations characterized by $v_0$.
