Non-relativistic Nambu-Goldstone modes associated with spontaneously   broken space-time and internal symmetries
  We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in non-relativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) sigma model, a magnetic domain wall in ferromagnets with an easy axis. 
Michikazu Kobayashi and Muneto Nitta
hep-th cond-mat.mtrl-sci hep-ph