New generalized and improved (G′/G)-expansion method for nonlinear evolution equations in mathematical physics

Solitary and Periodic Wave Solutions of the Fourth Order Boussinesq Equation Through the Novel Exponential Expansion Method

“…The solitary and periodic wave solutions of these equations have importance physical significance to observe the oscillatory behaviors in these relevant fields. In addition, there are several types of mathematical method have been used to search the exact traveling wave solutions of NPDEs, such as the (G'/G)-expansion method [1,2], new approach of (G'/G)-expansion method [3], novel (G'/G)-expansion method [4], new approach of generalized (G'/G)-expansion method [5], the tanh method [6][7][8][9], the Jacobi elliptic function method [10,11], the homogeneous balance method [12][13][14], the Hirota's method [15], the Homotpy perturbation technique [16], the improved F-expansion method [17], the sine-cosine method [18], the modified simple equation method [19], the Exp-function method [20,21], the exp (-Φ (ξ))-expansion method [22][23][24][25][26] and others.…”

Numerical simulation and solutions of the two‐component second order KdV evolutionarysystem

“…Nonlinear evolution equations are often used to describe some physical aspects that arise in the various fields of nonlinear sciences, such as plasma physics, quantum mechanics, biological sciences, chemistry, chemical physics, and so forth. Various powerful techniques have been formulated and used by different scholars to find the solutions of some NLEEs, such as the sine-Gordon expansion method [1][2][3], the generalized Kudryashov method [4,5], the extended tanh method [6,7], the new generalized and improved (G /G)-expansion method [8], the Jacobi elliptic function method [9,10], the improved Bernoulli subequation function method [11], the tanh method [12,13], the sine-cosine method [14], the Lie group analysis method [15][16][17], the homogeneous balance method [18], the modified simple equation method [19,20], the meshless method of radial basis functions [21], He's variational iteration method [22], the explicit multistep Galerkin finite element method [23], the differential quadrature based numerical method [24], the partitioned second-order method [25], the adaptive pseudo-transient-continuation-Galerkin methods [26]. In general, various efficient techniques have been implemented to explore the search for the solutions of the different kind of NLEEs [27][28][29][30][31][32][33][34][35][36][37][38].…”

Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

“…So, investigation of exact solutions of NLPDEs will help to understand these phenomena better [1]. Therefore, some researchers have used many powerful methods for obtaining exact solutions of nonlinear partial differential equations, such as inverse scattering method [2], Hirota's bilinear method [3], Backlaund transformation [4], Painleve expansion [5], F-expansion method [24], sine-cosine method [6], homogenous balance method [7,8], exp-function method [9,10], improved (G'/G)-expansion method [11,12,13,14,15], ansatz method [16], the first integral method [17,18,19,20], Kudryashov method, extended trial equation method [21], tanh function method [22,23], auxiliary equation method [25], differential transform method [26], homotopy perturbation technique [27] and so on.…”