Exact Analytical Solutions of Generalized Fifth-Order KdV Equation by the Extended Complex Method

Abstract

The recently introduced technique, namely, the extended complex method, is used to explore exact solutions for the generalized fifth-order KdV equation. Appropriately, the rational, periodic, and elliptic function solutions are obtained by this technique. The 3D graphs explain the different physical phenomena to the exact solutions of this equation. This idea specifies that the extended complex method can acquire exact solutions of several differential equations in engineering. These results reveal that the extended complex method can be directly and easily used to solve further higher-order nonlinear partial differential equations (NLPDEs). All computer simulations are constructed by maple packages.