Application of Exp-function method for nonlinear evolution equations with variable coefficients

Application of the Exp-function method to the (2+1)-dimensional Boiti–Leon–Pempinelli equation using symbolic computation

“…The Exp-function method was found to be one of the most effective methods to search for exact solutions of NPDEs [5,24,26,34,42]. It has been successfully extended by the authors [19,45] to study some nonlinear equations with variable coefficients. Moreover, being less restrictive and concise, it is modified by the researchers [12,13,46,47] to analyse some special nonlinear differential-difference equations.…”

Generalized solitary and periodic wave solutions to a (2+1)-dimensional Zakharov–Kuznetsov equation

“…However, in [41], it is shown that the Burgers' equation in which the odd and even-order derivative terms coexist can be solved by the Exp-function method. (iii) Being less restrictive, the Exp-function method can be extended to a wide class of equations such as NLEEs with variable coefficients [42,43], a KdV equation with forcing term [44], and nonlinear differentialdifference equations [45][46][47][48]. Furthermore, the Exp-function method is more applicable to discrete NLEEs than hyperbolic function method.…”

The Backlund Transformation of the Generalized Riccati Equation and Its Applications to the Nonlinear KPP Equation

“…Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. In recent decades, many effective methods have been established to obtain exact solutions of nonlinear PDEs, such as the inverse scattering transform [1], the Hirota method [2], the truncated Painlevé expansion method [3], the Bäcklund transform method [1,4,5], the exp-function method [6][7][8], the simplest equation method [9,10], the Weierstrass elliptic function method [11], the Jacobi elliptic function method [12][13][14], the tanh-function method [15,16], the ( / G) G′ expansion method [17][18][19][20][21][22], the modified simple equation method [23][24][25][26], the Kudryashov method [27][28][29], the multiple exp-function algorithm method [30,31], the transformed rational function method [32], the Frobenius decomposition technique [33], the local fractional variation iteration method [34], the local fractional series expansion The objective of this article is to use the Bäcklund transformation of the generalized Riccati equation to construct new exact traveling wave solutions of the following nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation [22,26,46]. [22] have discussed Equation (1.1) using the ( / G) G′ -expansion method and found its ex...…”