Newly formed center-controlled rouge wave and lump solutions of a generalized (3+1)-dimensional KdV-BBM equation via symbolic computation approach

Abstract

In this article, we investigate the generalized (3+1)-dimensional KdV-Benjamin-Bona-Mahony equation governed with constant coefficients. It applies the Painlevé analysis to test the complete integrability of the concerned KdV-BBM equation. The symbolic computational approach provides first-order, second-order rogue wave and lump solutions with center-controlled parameters. The rogue waves localized in space and time have a significant amplitude, and lumps are of rational form solution, localized decaying solutions in all space directions rationally. Utilizing a symbolic computation approach, we get the bilinear equation of the KdV-Benjamin-Bona-Mahony equation and show the center-controlled rogue waves and lumps. We employ the symbolic system software Mathematica to do the symbolic computations, form the first and second-order rogue waves, and lump solutions with appropriate values of constant coefficients. The KdV-Benjamin-Bona-Mahony equation analyses the evolution of long waves with modest amplitudes propagating in plasma physics and the motion of waves in fluids and other weakly dispersive mediums. Moreover, rogue waves and lumps occur in several scientific areas, such as fluid dynamics, optical fibers, dusty plasma, oceanography, water engineering, and other nonlinear sciences.