LAUSR

Abstract In this work, the soliton molecules, three soliton molecules and four soliton molecules are obtained for the new (3 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation by the velocity resonance mechanism which is a new resonance condition and the N-soliton solution. The interactions between these kinds of soliton molecules are studied analytically and numerically by some figures with selecting suitable parameters. The other kinds of waves such as dark-singular, periodic-singular and plane-wave solutions are investigated by e x p ( − Φ ( ζ ) ) expansion method for this model to understand the physical properties for this model. Also, the dynamics for these waves are presented by some graphics.