Abstract
A (2 + 1)-dimensional coupled nonlinear partial equation which possesses a Hirota bilinear form is introduced. Based on the Hirota bilinear form, two solitary waves are constructed. In the meanwhile, lump waves are derived by using a positive quadratic function. By combining an exponential function with a quadratic function, interaction solutions between a lump and a one-kink soliton, and between a bi-lump and a one-soliton solution are generated. Some special concrete interaction solutions are depicted in both analytical and graphical ways.