Lump solution, lump-stripe solution, rogue wave solution and periodic solution of the (2 + 1)-dimensional Fokas system

In this paper, the goal is to focus on the localized characteristics and dynamic behavior of lump solutions and interaction solutions for the (2 + 1)-dimensional complex systems. The (2 + 1)-dimensional Fokas system was considered as the research model in this paper, based on the Hirota bilinear method, and a series of new exact solutions were constructed by selecting some new test functions. Meanwhile, the conditions for ensuring the positivity of lump solutions are discussed. In addition, the localized characteristics and dynamic behavior of some interaction solutions are described through analysis and graphics, for example, interaction solution between a lump and stripe soliton pairs contains a rogue wave excited from stripe soliton pairs. The main novelty of this paper is that a series of new analytical solutions obtained can explain the interaction mechanism of nonlinear waves in nonlinear physics. It is hoped that our research results can play a certain promoting role in the study of nonlinear theory. The method adopted in this paper can also study high-dimensional and variable-coefficient nonlinear complex systems.