Quasi-periodic and non-periodic waves in the (2 + 1)-dimensional generalized Broer–Kaup system

For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the (2 + 1)-dimensional generalized Broer–Kaup system, including multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. From which, new quasi-periodic and non-periodic excitations for the system are studied by means of the Jacobi elliptic functions with the space–time-dependent modulus.