Explicit solutions of the 2 + 1-dimensional breaking soliton equation

Some new 2 + 1- and 3 + 1-dimensional models are proposed. The known 2 + 1-dimensional breaking soliton equation and these new multi-dimensional integrable models are decomposed into the compatible 1 + 1-dimensional KdV equation and its higher-order ones. General evolution pictures along various flows represented by the scattering coordinates and the Abel–Jacobi coordinates, respectively, are obtained, from which the explicit solutions, including N-soliton and algebro-geometric solutions, of the known 2 + 1-dimensional breaking soliton equation and these new multi-dimensional integrable models are derived.