Exact and explicit traveling wave solution to the time-fractional phi-four and (2+1) dimensional CBS equations using the modified extended tanh-function method in mathematical physics

Abstract

This current study’s primary aim is to discover new and exact traveling wave solutions to the time-fractional phi-four equation and the (2+1) dimensional Calogero–Bogoyavlanskil schilf (CBS) equation in the perspective of nonlinear traveling wave phenomena. The modified extended tanh-function method is imposed on the phi-four and the (2+1) dimensional CBS equations in this case. Consequently, lump, mixed lump, lump-periodic, lump-periodic-kink, kink, singular kink, kink soliton, periodic, and singular solutions are exhibited in trigonometric, hyperbolic, and rational function solutions. To enucleate, the underlying traveling​ structures, achieved solutions are established by making their dynamic comportment of the exact solutions presented in three-dimensional (3D), contour, and two-dimensional (2D) chart with computational software MATLAB. In terms of conformable derivative, fractional traveling wave transformation, and the applied procedure, all the exact solutions obtained are considered to be novel. To comprehend the physical processes, we have portrayed the figures of the estimated solutions.

Keywords

• Modified extended tanh-function method
• Conformable derivative
• Traveling wave solution
• Phi-four equation
• Calogero–Bogoyavlanskil Schilf equation
• Mathematical physics