COLLECTIVE DYNAMICS OF A DOMAIN WALL — AN OUTLINE by

which describes a static, planar domain wall stretched along the x = 0 plane. Here Φ0 = M/(2 √ λ) denotes one of the two vacuum values of the field Φ — the other one is equal to −Φ0. The parameter M can be identified with the mass of the scalar particle related to the field Φ. The corresponding Compton length l0 = M −1 gives the physical length scale in the model. Energy density for the planar domain wall (2) is exponentially localised in a vicinity of the x = 0 plane. The transverse width of the domain wall is of the order 2l0. The issue is time evolution of a non-planar domain wall. Such domain walls can be infinite, consider, e.g., locally deformed planar domain wall or a cylindrical domain wall. They can also be finite closed, e.g., like a sphere or a torus. We shall restrict our considerations to a single large, smooth