Dynamical Analysis of Nonlocalized Wave Solutions of 2 + 1 -Dimensional CBS and RLW Equation with the Impact of Fractionality and Free Parameters

Abstract

This study retrieves some new exact solutions to the $\left(2+1\right)$ -dimensional Calogero-Bogoyavlenskii-Schilf (CSB) equation and regularized long wave (RLW) equation in the context of nonlinear traveling wave phenomena. In this regard, the advanced $\exp \left(-\phi \left(\xi \right)\right)$ -expansion method is imposed to the $\left(2+1\right)$ -dimensional CBS and RLW equation, and consequently, rogue, kink, singular kink, periodic, singular, and multiple soliton solutions are exhibited in terms of trigonometric, hyperbolic, and rational function solutions. To enucleate the underlying nonlocalized traveling wave features, accomplished exact solutions are established by making their dynamic behavior of the exact solutions exhibited in three-dimensional (3D) and two-dimensional (2D) combined chart with the help of computational software Maple 18. All of our accomplished solutions are claimed to be new in the sense of conformable derivative, chosen a unique fractional type wave transformation, dynamical behavior of fractionally and free variable, and the imposed method on our preferred equations.