New exact solutions, dynamical and chaotic behaviors for the fourth-order nonlinear generalized Boussinesq water wave equation (Q2052024)

Summary: Based on the extended homogeneous balance method, the auto-Bäcklund transformation transformation is constructed and some new explicit and exact solutions are given for the fourth-order nonlinear generalized Boussinesq water wave equation. Then, the fourth-order nonlinear generalized Boussinesq water wave equation is transformed into the planer dynamical system under traveling wave transformation. We also investigate the dynamical behaviors and chaotic behaviors of the considered equation. Finally, the numerical simulations show that the change of the physical parameters will affect the dynamic behaviors of the system.