A generalized F-expansion method with symbolic computation exactly solving Broer–Kaup equations

Solitary waves in an elastic rod: analytical solutions

“…F-expansion method was extended later in different ways ( 3 and references cited therein). Recently Zhang et al 3,13,14 introduced a generalized F-expansion method to obtain new and more general (even non-traveling) exact solutions in which the restriction on ) ,..., , , ( t z y x ξ as merely a linear function and the restriction on the coefficients being constants (as in the case of the traveling wave) are removed. As a result these authors obtained many new exact non-traveling waves 3 .…”

Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation

“…Step 6. Since the general solutions of (6) have been well known for us, choose properly , , and in ODE 7such that the corresponding solution ( ) of it is one of Jacobi elliptic functions (see Appendices A, B, and C) [43][44][45].…”

“…The effort in finding exact solutions to nonlinear equations is important for the understanding of most nonlinear physical phenomena, for instance, the nonlinear wave phenomena observed in the fluid dynamics, plasma, and optical fibers [1,2]. Many effective methods have been presented such as homotopy analysis method [22], variational iteration method [23,24], tanh-function method [25][26][27], homotopy perturbation method [28][29][30], tanh-coth method [26,31,32], Exp-function method [33][34][35][36][37][38], Jacobi elliptic function expansion method [39][40][41][42], and F-expansion method [43][44][45][46]. The main objective of this paper is using F-expansion method to construct the exact traveling wave solutions for Wick-type stochastic Schamel KdV equations via the Wicktype product, Hermite transform, and white noise analysis.…”

New Periodic Wave Solutions for MNW Hierarchy with the Aid of Computerized Symbolic Computation

“…Since the Korteweg-de Vries (KdV) equation was solved by Gardner, Green, Kruskal and Miura [3], many effective methods have been proposed for nonlinear PDEs. One of the existing methods is the so-called extended F-expansion method [4] proposed by Wang et al Later, the extended F-expansion method [4] and its different improvements have received a wide range of applications, such as those in [5][6][7][8][9][10][11][12]. In this paper, the extended F-expansion method [4,13] is employed to solve Eq.…”