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

• Published in: Physics letters. A Vol. 454; p. 128503
• Main Authors: Saifullah, Sayed, Ahmad, Shabir, Alyami, Maryam Ahmed, Inc, Mustafa
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 05.12.2022
• Subjects: Hirota bilinear method; Kink solution; Lump solution; Periodic soliton; Kink solution; Lump solution; Hirota bilinear method; Periodic soliton
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2022.128503

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. •The generalized perturbed Korteweg–de Vries (KdV) equation is considered.•The Hirota bilinear method and Cole-Hopf transformation is used.•The lump and kink-soliton solutions are presented.•The obtained results are given by figures.