Investigation of lump, soliton, periodic, kink, and rogue waves to the time-fractional phi-four and (2+1) dimensional CBS equations in mathematical physics

Abstract In this article, we investigate the lump, soliton, periodic, kink, and rogue waves to the time-fractional phi-four and (2+1) dimensional Calogero-Bogoyavlanskil schilf (CBS) equations. The (G′/G,1/G)-expansion technique is applied to obtain the solutions of the phi-four and Calogero-Bogoyavlanskil schilf (CBS) equations with the contribution of conformable derivative. The stated method declines a huge volume of calculation. The (G′/G,1/G)-expansion technique is also known as the two-variable method. Consequently, lump, mixed lump, soliton, bell-shaped soliton, periodic, kink, periodic-kink, singular kink, rogue wave solutions are displayed in hyperbolic and trigonometric function solutions. Varieties of other traveling wave solutions are also formulated with the mentioned method. Moreover, for the physical explanation of the obtained solutions, the three-dimensional (3D) surface plots, contour plots combined with 3D surface plots, and two-dimensional (2D) plots are presented using the computer software MATLAB. Additionally, it is possible to deduce that the obtained solutions and their physical properties will aid in the understanding of water wave circulation in nonlinear dynamics.