A new note on a homogeneous balance method

Exact soliton solutions of the modified KdV–KP equation and the Burgers–KP equation by using the first integral method

“…In order to better understand these nonlinear phenomena, many mathematicians and physical scientists make efforts to seek more exact solutions of them. Several powerful methods have been proposed to obtain exact solutions of nonlinear evolution equations, such as multiple exp-function method [1], tanh-sech method [2][3][4][5], extended tanh method [6][7][8][9], hyperbolic function method [10], sine-cosine method [11][12][13], Jacobi elliptic function expansion method [14], F-expansion method [15], transformed rational function method [16], homogeneous balance method [17][18][19][20][21][22] and so on.…”

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(<i>ξ</i>))-Expansion Method

“…Balancing the higher order derivative of u′′′′ and the nonlinear term 3 u appearing in (9), we obtain 2 N = . Therefore, the Equation (9) has the following form of solution: …”

“…Therefore, it is necessary to solve them analytically or numerically. Some of the methods to solve them analytically are the Hirota method [1], the projective Riccati equation method [2], the homogeneous balance method [3]- [5], the tanh-function method [6]- [10], the exp-function method [11], the improved F-expansion method [12], the ( ) ( ) exp ξ −Φ -expansion method [13]- [19], sine-cosine method [20], the modified simple equation method [21], the ( ) G G ′ -expansion method [22] [23], the modified extended tanh-function method with Riccati equation [24] and others. In the references [13]- …”

New Exact Solutions of the (2+1)-Dimensional Ginzburg-Landau Equation

“…With the rapid development of nonlinear science based on computer algebraic system like Maple package, some new powerful solving methods have been developed, such as multi-wave method [7] homogeneous balance principle [8][9][10], F-expansion method [11][12], extended auxiliary equation method [13][14], and so on.…”