Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger-type equations

On the new wave behavior of the Magneto-Electro-Elastic(MEE) circular rod longitudinal wave equation

“…2 )expansion method [2], the extended tanh method [3], the jacobi elliptic function method [4], the homogeneous balance method [5], the generalized Kudryashov method [6], the generalized (G ′ /G) method [7], the extended homoclinic test function method [8], the improved Bernoulli sub-equation function method [9], the improved exp (−Φ(ξ))expansion function method [10] and so on. In general, many more analytical techniques have been designed and used in obtaining analytical solutions of different NLEs [11][12][13][14][15][16][17][18][19][20][21][22].…”

Solitons and Other Solutions for Two Higher-Order Nonlinear Wave Equations of KdV Type Using the Unified Auxiliary Equation Method

“…In recent years, quite a few methods for constructing explicit and solitary wave solutions of these nonlinear evolution equations have been presented. A variety of powerful methods, such as the semi-inverse variational method [1][2][3][4][5], the exp-function method [6][7][8], the Jacobi elliptic function method [9][10][11][12], the (G /G)expansion method [13,14], the Kudryashov method [15][16][17], the multiple exp-function method [18,19], the modified simple equation method [20][21][22], the auxiliary equation method [23,24], the extended auxiliary equation method [25][26][27][28], the soliton ansatz method [29][30][31][32][33][34][35], the traveling wave hypothesis [36], the unified auxiliary equation method [37,38], the conformable fractional derivatives [39][40][41], the Collocation finite element method [42] and so on.…”

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

“…So it is interesting to seek new exact solutions for Equation 2. The Jacobi elliptic function method 20,21 and the F-expansion method [22][23][24][25][26] are straightforward and concise symbolic computation methods, which help ones to find rich solutions for nonlinear evolution systems. 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.…”