Complex wave excitations and their interaction behaviors for higher-dimensional nonlinear model

Taking an approach by means of a special variable separation, some novel and interesting localized (3+1)-dimensional excitations, including embedded-soliton, taper-like soliton, plateau-type soliton and rectangle-soliton, were revealed thanks to the intrusion of appropriate boundary conditions and/or initial qualifications. The properties of the complex wave excitations in the periodic wave background and their interactions were investigated, showing some novel features or interesting behaviors.