Homoclinic breather wave, rouge wave and interaction solutions for a (3+1)-dimensional KdV-type equation

Based on symbolic computations, homoclinic breather wave, rouge wave and interaction solutions to the (3+1)-dimensional KdV-type equation are constructed. Two homoclinic breather solutions and a rouge wave solution are obtained by using the extended homoclinc test. Subsequently, we study interaction solutions between a lump solution and 1-kink soliton or 2-kink soliton of the KdV-type equation. In addition, periodic interaction solutions of the KdV-type equation are also studied. Moreover, dynamics behavior of these obtained solutions are exhibited using graphical analysis. (paper)