The global domain of attraction and the initial value problems of a kind of GKdV equations

The initial value problem of a kind of Generalized Korteweg–de Vries (GKdV) equations are considered by using Sobolev space theory and finite element method. The well-posedness of the solution of the GKdV equation is obtained. Simple cell mapping method is employed to obtain the global domain of attraction and the finite step domain of attraction of GKdV equations.