Evolution of breathers and interaction between high-order lump solutions and N-solitons (N → ∞) for Breaking Soliton system.

By employing the Hirota's bilinear method and different test functions, we investigate different forms of breather solitons and some new lump solutions of the (2+1)-dimensional Breaking Soliton system. During this process, some new nonlinear phenomena, such as degeneration of breather solitons, evolution of double breathers and emergence of lump solutions, are studied and shown. Besides, some interaction solutions between high-order lump solutions and N -soliton solutions (N → ∞) are studied. We construct the existence theorem of the interaction solutions and give a detailed proof process for the first time. Some different types of interaction solutions are used as concrete examples to illustrate the effectiveness of the described theorem, such as rational-exponential type, rational-cosh-cos type, rational-logarithmic type, and some three-dimensional spatial structure figures are simulated and displayed to reflect the evolutionary behavior of the interaction solutions with the increase of soliton number N. • Some different forms of breathers and lump solutions are obtained. • The existence theory of interaction between lump and N solitons is proved. • Some new nonlinear phenomena and spatial structures are reported. • Some different types of interaction solutions are simulated and displayed. [ABSTRACT FROM AUTHOR]