Nonlinear dynamics behavior of the (2+1)-dimensional Sawada–Kotera equation

In this paper, we mainly analyze the nonlinear dynamics behavior of the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera (S–K) equation, which can be usually used to describe shallow water phenomena from natural science. First, the multiple resonant wave and complexiton solutions are constructed with the help of the linear superposition principle, under different domain fields, such as real and complex domain fields, respectively. Next, we apply a new ansatz method to obtain a class of rogue wave solutions (one-rogue wave and two-rogue wave solutions). Finally, the 3-dimensional and 2-dimensional density graphs are plotted for the yielded results in the above texts to better illustrate the dynamics processes to them.