Higher rogue and rogue-soliton interaction solutions of a (2 + 1) dimensional nonlinear model in fluid mechanics

Abstract

In this study, two new theorems are generalized. We obtained a new paradigm about the second order rogue wave and multiple exponential functions, and a new paradigm about the second order rogue wave and multiple hyperbolic cosine functions. Six sets of interaction solutions of the model are solved by means of symbolic calculation and two new theorems. Meaningful graphs of the propagation processes along time demonstrated the interaction phenomena for these solutions. The energy transfer process can be observed when the second order rogue waves interact with multiple exponential functions or multiple hyperbolic cosine functions. As a conclusion from our paper, the solitons’ energy transfers to the second order rogue wave at beginning, the rogue wave’s energy dissipates and transfers to the solitons along the time moving. It will contribute to the research on the generation of rogue waves.