Observation of interaction phenomena for two dimensionally reduced nonlinear models

To study the lump-soliton interaction phenomenon for the (3+1)-dimensional nonlinear model with dimensional reduction, interaction solutions have been formulated by combining positive quadratic functions with hyperbolic function in bilinear equations. The collision between lump and soliton has been analyzed and simulated. When the lump is induced by a bounded twin soliton, the rogue wave turns up, which can only be visible at an instant time. Based on the solutions, it is easy to find the amplitude, the place and the arrival time of the rogue waves. The mechanism investigated in this paper may shed some light on the study of rogue waves in oceanography, fluid dynamics and nonlinear optics.