Exact solutions for the generalized KdV equation by using Backlund transformations

In this paper, the Backlund transformations for the generalized KdV equation are constructed through Ablowitz–Kaup–Newell–Segur (AKNS) system in using Ricattiʹs form of the inverse method. The derived Backlund transformations are used to generate new classes of exact solutions. The technique developed here is based on the construction of wave functions which are the solutions of the associated AKNS. From known simple solutions we shall construct other solitons and wave solutions as well.