Simplest exp-function method for exact solutions of Mikhauilov-Novikov-Wang equations

Abstract

In this paper, the simplest exp-function method which combines the exp-function method with a direct algorithm is used to exactly solve the Mikhauilov-Novikov-Wang equations. As a result, two explicit and exact solutions are obtained. It is shown that the simplest exp-function method provides a simpler but more effective mathematical tool for constructing exact solutions of non-linear evolution equations in fluids.

Variational principle for non-linear fractional wave equation in a fractal space

“…We will adopt the two-scale method [21][22][23][24] and the exp-function [25][26][27][28][29][30][31] to solve the fractional nonlinear wave equation. The two-scale transform [21][22][23][24] is an excellent tool to dealing with fractional differential equations in fractal space.…”

“…The two-scale transform [21][22][23][24] is an excellent tool to dealing with fractional differential equations in fractal space. The exp-function method [25][26][27][28][29][30][31] was proposed by Ji-Huan He, it is a powerful tool to finding approximate solutions of fractional differential equations. When…”

“…This paper is to establish a variational formulation for Eq. (1.1) using the semi-inverse method [1][2][3][4][5][6][7][8][9][10], and the two-scale transform [21][22][23][24] and the exp-function method [25][26][27][28][29][30][31] are used to find the approximate analytical solution of Eq. (1.1).…”

“…According to the definition of He's fractal derivative, eq. (3We adopt He's exp-function method[25][26][27][28][29][30][31] to solve eq. (3where  and  are real numbers.…”

Exact solutions of space-time fractional (2+1)-dimensional breaking soliton equation

“…In the past decades, many methods have been developed to obtain exact solutions of fractional-order NPDEs. Some of the most important methods are the homotopy perturbation method [1][2][3], the variational iteration method [4][5][6][7][8][9], and the exp-function method [10][11][12][13].…”