WITHDRAWN: Lump, lump with damped oscillation, double cross kinky lump with oscillation, collision of kinky and breather wave solutions to a broadened Hietarinta-like equation

Abstract

One of the most significant solutions to linear and nonlinear partial differential equations is a lump soliton as it has seismic wave nature. Realizing seismic natures of such lump and oscillating lump wave, one can take initiative to mitigate its harmful energies by opposite external periodic forces. The main purpose of this study is to demonstrate various lump solutions from kinky breather-wave. In this regard, the Hirota bilinear scheme and the enhanced homoclinic test procedure are utilized to get kinky breather-wave solutions with second-order linear dispersive components that can be produced by a fourth-order nonlinear term of the Hietarinta-like equation. By making particular values of certain parameters, we derived bright- dark lump solitons from kinky-breather propagation wave solutions in a specific scenario. The cross-kinky wave in breather form, lump with damped oscillation, kink with damped oscillation, as well as lump solutions are also obtained from the Hirota bi-linear scheme constructing breather waves. A set of 3D, 2D and density graphs are used to investigate such dynamical behaviors of model numerically. These patterns are also illustrated numerous clarifications for others prototypes in the purviews of nonlinear science and engineering.