Theory for the spatio-temporal dynamics of domain walls close to a nonequilibrium Ising-Bloch transition

A crucial ingredient determining the dynamical evolution of domain walls is their interaction. While the interaction between Ising fronts has been widely studied in the literature, leading to the formation of localized structures (LS) or dissipative solitons in a wide range of complex systems, only specific cases concerning the interaction of Bloch walls have been considered. In this work we show that the interaction of Bloch walls can be very generally described in terms of only two coupled modes of the front, the neutral (or Goldstone) mode and the chiral mode that become unstable at the Ising-Bloch (IB) transition. Our generic results predict, close to an IB transition, the existence of stationary Ising and Bloch LS, drifting Bloch LS, oscillating (breathing) LS, and bouncing walls, and explain complex behavior observed in different physical system.