Abstract
The aim of this manuscript is to find the analytical solutions of the Korteweg-de Vries (KdV) equation with dual power law nonlinearity using the exp-function method. The KdV equation is used to study the shallow water wave behavior of long wavelengths and small amplitude. With the help of the exp-function method, a variety of exact wave solutions of the KdV equation are obtained including kink, anti-kink, and bell-shaped traveling wave solutions. The various kinds of solutions to the considered nonlinear KdV equation may help to explore the relevant nonlinear phenomena in fluid dynamics. The presented results are novel and the KdV equation with dual power law nonlinearity has been evaluated using the presented technique for the first time in this work. In addition, some of the exact solutions have been shown by contour planes, 3D plots, and 2D graphics for visualizing the underlying dynamics of the results.