Resonant Solutions and Rogue Wave Solutions to the (2+1)-Dimensional Caudrey–Dodd–Gibbon Equation

The (2+1)-dimensional Caudrey–Dodd–Gibbon (CDG) equation, which can frequently be used to be describe the propagations of shallow-water waves and plasma physics, is solved by various methods in this paper, thereby revealing its nonlinear dynamical behavior. First, through the linear superposition principle in conjunction with symmetric Hirota bilinear method, we obtain a bilinear form of the CDG equation, which possesses several symmetry properties, and construct the resonant solutions to exponential waves. Then, the one-rogue wave solutions to the CDG equation are constructed via the ansatz method. Finally, we show three-dimensional diagrams and density graphs of the yielded solutions to better show the dynamic characteristics.