The -expansion method for the nonlinear lattice equations

The Mapping Method for Solving a New Model of Nonlinear Partial Differential Equation

“…Let u(x, t) = u(ξ), ξ = µ (x − ct) then equation (1) reduces to a nonlinear ordinary differential equation (ODE)…”

“…In order to get exact solutions directly, many powerful methods have been introduced such as the G ′ G -expansion method [1], inverse scattering method [2,3], Hirota's bilinear method [4,5], the tanh method [6,7], the sine-cosine method [8,9], Backlund transformation method [10,11], the homogeneous balance [12,13], Darboux transformation [14], the Jacobi elliptic function expansion method [15].…”

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...…”

On The Exact Solutions to Conformable Time Fractional Equations in EW Family Using Sine-Gordon Equation Approach

“…Exp function method [7,8] assumes the predicted solutions as a finite series of some particular functions. (G /G) expansion method [9,10] is an alternative that approaches the solution with a finite power series of a function satisfying a particular ODE. Trigonometric and hyperbolic type solutions to nonlinear PDEs can be determined by implementation of sine-cosine approach [11][12][13].…”