Symmetries and solutions of the three-dimensional Kadomtsev–Petviashvili equation

A group of point transformations permitted by the three-dimensional Kadomtsev–Petviashvili equation is calculated. An example of an invariant solution is given. Exact solutions for the equation under study in the form of double waves are found. The resulting solutions are expressed in terms of elementary functions and describe the interaction of a pair of solitons. Smooth bounded rational solutions are also constructed.