New Applications of the (G'/G,1/G)-Expansion Method

Abstract

In this paper, we study general solutions of the new fth order nonlinear evolution and the Burgers KP equations with the aid of the two variables (G /G, 1/G)-expansion method. The kink, bell-shaped solitary wave, periodic and singular periodic solutions are obtained. Finally, the numerical simulations add to these obtained solutions.

Multi-Peak and Bright-Dark Solitary Wave Solutions of Higher-Order Dispersive Nonlinear Schrödinger Equations and their Applications

“…In recent years, A large number of scholars have been devoted to constructing exact solutions of the NLSEs in different ways [17][18][19], and several effective techniques have been used to find and analyze solutions, such as: F-expansion method, modified F-expansion scheme, direct algebraic, modifiedjextended direct algebraic scheme, extended tanh method, exp-functionjmethod, auxiliary equation method, Jacobijelliptic functionjmethod, rational expansionjmethod, simple equationjmethod, modified simple equation method and even more. Some scholars also focus on the character and stability of solutions [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Optical Solutions of the Kundu-Eckhaus Equation Via Two Different Methods

“…The analytical expressions of NLEEs were researched using various powerful techniques. Some of these methods are Auto-Backlund transformations [1], modified simple equation method [2], transformed rational function method [3], trial method [4], the sine-Gordon expansion method [5], the (G'/G)-expansion method [6], (G'/G,1/G)-expansion method [7], auxiliary equation method [8,9], exp-function method [10], F-expansion method [11], sine-cosine method [12], ansatz method [13], sub equation method [14], exponential rational function method [15], Lie group analysis [16], Hirota bilinear method [17], Backlund transformation method [18], Wronskian technique [19], homogeneous balance method [20], inverse scattering method [21], and so on [22]. Regarding the domain of research in photonics sciences, optical solitons is considered among the most rapidly emerging fields.…”

Further fresh and general traveling wave solutions to some fractional order nonlinear evolution equations in mathematical physics

“…Therefore, it has become the core aim in the research area of fractional related problems that how to develop a stable approach for investigating the solutions to FNLEEs in analytical or numerical form. Many researchers have offered different approaches to construct analytic and numerical solutions to FNLEEs as well as integer order and put them forward for searching traveling wave solutions, such as the He-Laplace method [10], the exponential decay law [11], the reproducing kernel method [12], the Jacobi elliptic function method [13], the À G 0 =G Á -expansion method and its various modifications [14][15][16][17][18], the exp-function method [19], the sub-equation method [20,21], the first integral method [22], the functional variable method [23], the modified trial equation method [24], the simplest equation method [25], the Lie group analysis method [26], the fractional characteristic method [27], the auxiliary equation method [28,29], the finite element method [30], the differential transform method [31], the Adomian decomposition method [32,33], the variational iteration method [34], the finite difference method [35], the homotopy perturbation method [36] and the He's variational principle [37], the new extended direct algebraic method [38,39], the Jacobi elliptic function expansion method [40], the conformable double Laplace transform [41] etc. But each method does not bear high acceptance for the lacking of productivity to construct the closed form solutions to all kind of FNLEEs.…”