Dynamical analysis and explicit traveling wave solutions to the higher-dimensional generalized nonlinear wave system

For dealing with exact solutions and properties of PDEs, the higher-dimensional equations are far more complicated than the lower dimensional ones. In the current paper, by using the dynamical system method, we study the (n+1)-dimensional generalized nonlinear coupled KdV (c-KdV) system, which includes a lot of important c-KdV types of systems as its special case. The bifurcations and phase portraits of the nonlinear PDE system are investigated, then we give the explicit parametric representations of all possible solitary wave solutions and periodic wave solutions under different parametric conditions.