Dynamics Behavior of Lumps and Interaction Solutions of a (3+1)-Dimensional Partial Differential Equation.

In this work, we investigate a linear partial differential equation in (3+1)-dimensions. We construct lump solutions which localize in all directions in the (x,y,z)-space. By combining the trigonometric, hyperbolic and exponential functions with a quadratic function, diversity interaction solutions such as interacted lumps with periodic waves and interacted lumps with multisoliton are generated. The phenomena of interaction solutions between a lump and a multisoliton and between a lump and a multikink soliton are presented by figures. The results expand understanding dynamical behavior of the (3+1)-dimensional partial differential equations.