Exact Traveling Wave Solutions of a Higher-Dimensional Nonlinear Evolution Equation

Abstract

The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh-coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

Exact travelling wave solutions for some important nonlinear physical models

“…In particular, there has been considerable interest in seeking exact travelling wave solutions of nonlinear evolution equations that describe some important physical and dynamic processes. In the past several decades, many powerful methods such as variational iteration method [1], homotopy analysis method [2], homotopy perturbation technique [3], modified tanh-coth method [4], the Jacobi elliptic function method [5], (G /G)-expansion method [6][7][8], the expfunction method [9][10][11][12], trial equation method [13], spectral collocation method [14] and many other techniques were used to obtain exact travelling wave solutions of nonlinear problems. More precisely, there is no unified method that can be used to handle all types of nonlinear problems.…”

Direct approach for solving nonlinear evolution and two-point boundary value problems

“…Accurate and fast numerical solution of nonlinear equations is of great importance due to their wide applications in scientific and engineering research. Different numerical methods have been proposed by various authors for solving nonlinear problems such as exp-function method [1][2][3][4][5][6], Jacobi elliptic function method [7], variational iteration method [8,9], tanh function method [10,11], (G /G)expansion method [12], homotopy perturbation method [13][14][15] and so on. However, practically there is no unified method that can be used to handle all types of nonlinearities.…”

Explicit solutions for couple higher order nonlinear Schrödinger equation by (G′G)-expansion method

“…Various powerful methods have been presented to find the exact solutions of nonlinear partial differential equations, for example, several important techniques have been developed such as the tanh-method [1,2], sine-cosine method [3,4], tanh-coth method [5], exp-function method [6], homogeneous-balance method [7,8], Jacobi-elliptic function method [9,10], first-integral method [11,12] and so on, all the methods have some limitations in their applications. In fact, there is no unified method that can be used to handle all types of nonlinear partial differential equations (NLPDE).…”