New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using Extended F-Expansion Method

Abstract

The F-expansion method is used to find traveling wave solutions to various wave equations. By giving more solutions of the general subequation, an extended F-expansion method is introduced by Emmanuel. In our work, a generalized KdV type equation of neglecting the highest-order infinitesimal term, which is an important water wave model, is discussed by using the extended F-expansion method. And when the parameters satisfy certain relations, some new exact solutions expressed by Jacobi elliptic function, hyperbolic function, and trigonometric function are obtained. The related results are enriched.

Exact Solutions for(4+1)-Dimensional Nonlinear Fokas Equation Using ExtendedF-Expansion Method and Its Variant

“…In [37], we have successfully applied the extended Fexpansion method on a higher-order wave equation of KdV type. In this work, we apply this method and its variant on (4 + 1)-dimensional nonlinear Fokas equation for obtaining new exact traveling solutions.…”

Joint Application of Bilinear Operator and F-Expansion Method for (2+1)-Dimensional Kadomtsev-Petviashvili Equation

“…Substituting (18) and (19) into (3) and collecting the coefficients of , ( ), and ( ), one yields a nonlinear algebraic system of parameters ℎ 0 , ℎ 1 , ℎ 2 , 1 , 2 , 1 , 2 , 1 , and 2 . In particular, ℎ 0 = − , ℎ 1 = + , and ℎ 2 = −1 are taken to solve the nonlinear algebraic system whose and are undetermined constants; we obtain…”

“…To understand the inherent essence and evolution mechanism of these nonlinear traveling waves, seeking the exact traveling wave solutions has been recognized. In recent years, much efforts have been spent on this task and many significant methods have been established such as variational iteration method [8], homotopy perturbation method [9,10], Fan subequation method [11,12], exp-function method [13], Hirota's bilinear method [14,15], / -expansion method [16,17], and F-expansion method [18][19][20][21]. In most of the existing literature, authors always study the improvement of the adopted method to obtain more forms of solutions.…”

A series of the solutions for the Heisenberg ferromagnetic spin chain equation

“…The improved F-expansion method was proposed to find more abundant traveling wave solitions, which is based on the F-expansion and Exp-function method. [27][28][29] The main objective of this work is to seek new exact solutions for Equation 2. A series of abundant exact solutions, namely, periodic and doubly periodic wave solutions, solitary wave solutions, are obtained by using the Jacobi elliptic function method and improved F-expansion method.…”