Nonlinear Superposition Between Lump Waves and Other Nonlinear Waves of the (2+1)-Dimensional Extended Korteweg-De Vries Equation

In this study, we consider an extended (2+1)-dimensional KdV equation, which is used to simulate the propagation and evolution of nonlinear waves. Based on the N-soliton solutions, a new constraint is imposed on the parameters, and the novel nonlinear superposition for the lump wave with solitons, breathers of the equation are studied by combining the long wave limit and the complex conjugate of the parameters. Furthermore, with the aid of the velocity resonance method, the lump-soliton molecule and the interaction solution of the molecule and soliton are obtained. The physical dynamics of these solutions are illustrated in the form of graphical illustrations.