Multiple bifurcation solitons, lumps and rogue waves solutions of a generalized perturbed KdV equation

Abstract

The perturbed KdV equation has many applications in mechanics and sound propagation in fluids. The aim of this manuscript is to study novel crucial exact solutions of the generalized perturbed KdV equation. The Hirota bilinear technique is implemented to derive general form solution of the considered equation. The novel soliton solutions are studied by taking different dispersion coefficients. We analyse first- and second-order soliton solutions, multiple-bifurcated soliton solutions, first- and second-order lump and rogue wave solutions of the considered equations. We show the effect of the parameters on the evolution of soliton solutions of the considered equation. All the obtained results are simulated by using MATLAB-2020.