Exact solutions for Calogero–Bogoyavlenskii–Schiff equation using symmetry method

The Multiple Exp-Function Method and the Linear Superposition Principle for Solving the (2+1)-Dimensional Calogero–Bogoyavlenskii–Schiff Equation

“…The objective of this article is to apply two interesting methods, namely, the multiple exp-function method and the linear superposition principle to construct the exact solutions for the following (2+1)-dimensional CalogeroBogoyavlenskii-Schiff (CBS) equation [40][41][42]:…”

“…Recently, a large amount of literature has been provided to construct the solutions of the PDEs. Several powerful methods have been proposed to obtain approximate and exact solutions of these equations, such as the inverse scattering transform [1], the Bäcklund transformation method [2], the Hirota bilinear method [3], the Adomian decomposition method [4,5], the variational iteration method [6][7][8], the homotopy analysis method [9][10][11][12], the homotopy perturbation method [13][14][15], the Lagrange characteristic method [16], the fractional sub-equation method [17], the (G′/G)-expansion method [18,19], the transformed rational function method [20], the multiple exp-function method [21,22], the generalised Riccati equation method [23], the Frobenius decomposition technique [24], the local fractional differential equations method [25,26], the local fractional variation iteration method [27], the multiple (G′/G)-expansion method [28], the cantor-type cylindrical coordinate method [29], the Riccati equation method combined with the (G′/G)-expansion method [30], the fractional complex transform method [31], the modified simple equation method [32][33][34][35], the first integral method [36][37][38], the linear superposition principle …”

Investigation of exact traveling wave solution for the (2+1) dimensional nonlinear evolution equations via modified extended tanh-function method

“…Recently, some special cases of Eq. (1) have been studied by several authors [18,[38][39][40]. The rest of this paper is organized as follows: In section 2, the modified extended tanh-function method is discussed in details.…”

Exact solutions of the Biswas-Milovic equation, the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method

“…In recent years, a number of powerful and efficient methods for finding analytic solutions to nonlinear equations have drawn a lot of interest by a diverse group of scientists. These include, for example: Hirota's bilinear transformation method [1,2]; the tanh-function method [3,4]; the (G ′ /G)-expansion method [5][6][7][8][9][10]; the Exp-function method [11][12][13][14]; the multiple exp-function method [15][16][17]; the symmetry method [18,19]; the modified simple equation method [20][21][22]; the improved (G ′ /G)-expansion method [23]; a multiple extended trial equation method [24]; the Jacobi elliptic function expansion method [25,26]; the Bäcklund transform method [27,28]; the generalized Riccati equation method [29]; the modified extended Fan sub equation method [30]; the auxiliary equation method [31,32]; the first integral method [33,34]; the modified Kudryashov method [35][36][37][38][39][40][41][42], and the soliton ansatz method . The objective of this paper is to apply the generalized Kudryashov method …”