Mechanisms of nonlinear wave transitions in the (2+1)-dimensional generalized breaking soliton equation

We study the transformed nonlinear waves of the (2+1)-dimensional generalized breaking soliton (gBS) equation by analyzing characteristic lines. The N-soliton solution of the gBS equation is obtained by virtue of the Hirota bilinear method, from which the 1-order and 2-order breather wave solutions of the gBS equation are derived by the complexification method. Then, we obtain the condition of the breather wave transformation analytically. Under the condition that the two characteristic lines of the 1-order breather wave are parallel to each other, we show that the 1-order breather wave can be converted into many other types of nonlinear waves, such as M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, quasi-periodic soliton, etc. Moreover, we give four deformation modes of the 2-order breather wave, including intersection mode of a transformed wave and a breather wave; parallel mode of a transformed wave and a breather wave; intersection mode of two transformed waves; parallel mode of two transformed waves. Finally, we present the graphical analysis of the resulting solutions in order to better understand their dynamical behaviors.