Analysis of interaction of lump solutions with kink-soliton solutions of the generalized perturbed KdV equation using Hirota-bilinear approach

Abstract

Using the Hirota bilinear method (HBM) and Cole-Hopf transformation, we extract the interaction between the lump and kink-soliton solutions for the generalized perturbed Korteweg–de Vries (KdV) equation in this manuscript. In the literature [15], the authors have applied the Cole-Hopf transformation with a value of R to study the particular case of the generalized perturbed KdV equation, which is found to be an inappropriate value. Alqarni et al., computed an appropriate value of R in the literature [29]. We use the correct value of R and get more clearly the outcomes for a lump-single kink soliton, a lump-two kink soliton, and a lump-periodic soliton solution. We display these solutions in 2D and 3D space using Mathematica by selecting the proper values for the parameters.