Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation by means of Hirota's bilinear method

In this paper, we implement the Hirota's bilinear method to extract diverse wave profiles to the generalized perturbed-KdV equation when the test function approaches are taken into consideration. Several novel solutions such as lump-soliton, lump-periodic, single-stripe soliton, breather waves, and two-wave solutions are obtained to the proposed model. We conduct some graphical analysis including 2D and 3D plots to show the physical structures of the recovery solutions. On the other hand, this work contains a correction of previous published results for a special case of the perturbed KdV. Moreover, we investigate the significance of the nonlinearity, perturbation, and dispersion parameters being acting on the propagation of the perturbed KdV. Finally, our obtained solutions are verified by inserting them into the governing equation.