Dynamic behaviors of the lump solutions and mixed solutions to a (2+1)-dimensional nonlinear model

In this paper, we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended (2+1)-dimensional shallow water wave equation, which is linked with a novel (2+1)-dimensional nonlinear model. This model might be applied to describe the evolution of nonlinear waves in the ocean. Under the effect of a novel combination of nonlinearity and dispersion terms, two cases of lump solutions to the (2+1)-dimensional nonlinear model are derived by searching for the quadratic function solutions to the bilinear form. Moreover, the one-lump-multi-stripe solutions are constructed by the test function combining quadratic functions and multiple exponential functions. The one-lump-multi-soliton solutions are derived by the test function combining quadratic functions and multiple hyperbolic cosine functions. Dynamic behaviors of the lump solutions and mixed solutions are analyzed via numerical simulation. The result is of importance to provide efficient expressions to model nonlinear waves and explain some interaction mechanism of nonlinear waves in physics.

Automated summary

In this paper, a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended (2+1)-dimensional shallow water wave equation is proposed, linked with a novel (2+1)-dimensional nonlinear model. Two cases of lump solutions to the (2+1)-dimensional nonlinear model are derived, as well as one-lump-multi-stripe and one-lump-multi-soliton solutions. Dynamic behaviors of the solutions are analyzed through numerical simulation. The results contribute to efficient expressions for modeling nonlinear waves and explaining interaction mechanisms in physics.