  Domain wall solitons are the simplest topological objects in field theories.
The conventional translational symmetry in a field theory is the generator of a
one-parameter family of domain wall solutions, and induces a massless moduli
field which propagates along a domain wall. We study similar issues in braided
noncommutative field theories possessing Hopf algebraic translational
symmetries. As a concrete example, we discuss a domain wall soliton in the
scalar phi^4 braided noncommutative field theory in Lie-algebraic
noncommutative spacetime, [x^i,x^j]=2i kappa epsilon^{ijk}x_k (i,j,k=1,2,3),
which has a Hopf algebraic translational symmetry. We first discuss the
existence of a domain wall soliton in view of Derrick's theorem, and construct
explicitly a one-parameter family of solutions in perturbation of the
noncommutativity parameter kappa. We then find the massless moduli field which
propagates on the domain wall soliton. We further extend our analysis to the
general Hopf algebraic translational symmetry.
