An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

“…The study of exact solutions of such mathematical models is the most exciting area of research investigation. To obtain the exact solutions of such mathematical models, recently, researchers follow different analytical methods, such as tangent hyperbolic method [2], modified extended direct algebraic method [3,4], ðG′/G 2 Þ -expansion method [5], Kudryashov method [6], Lie symmetry method [7], extended trial equation method [8], singular manifold method [9], sinh-Gordon expansion method [10], ðG′/GÞ-expansion method [11], generalized ð G′/GÞ-expansion method [12], generalized-improved ðG′/ GÞ-expansion method [13], extended generalized ðG ′ /GÞ -expansion method [14,15], and ðG′/G, 1/GÞ expansion method [16].…”

“…Out of these methods, the extended generalized ðG′/GÞ -expansion method [14,15] is a well-defined, simple, and effective method. It is based on initial assumption solution, which can be written in terms of polynomial of ðG′/GÞ with variable coefficients, and also, G = GðβÞ satisfies [14]…”

“…where Q 1 ≠ 0, Q 2 , Q 3 , and Q 4 are constants. The Schamel, the Schamel Burgers [14], and modified Korteweg-De Vries (KdV) [15] equations are solved by the extended generalized ðG ′ /GÞ-expansion method and obtained the shock waves, periodic waves, and multiwaves. The generalized ZK equation with variable coefficients is written in the form of [17,18]…”

New analytical solutions to the stochastic (2 + 1)-dimensional combined KdV-mKdV equation

“…In recent years, nonlinear partial differential equations (NPDEs) have gained significant relevance in the study of nonlinear phenomena due to their prevalence across various scientific and engineering fields, such as Geophysics [13], Quantum Mechanics [3], Nonlinear Optics [19], Condensed matter Physics [9] A variety of powerful methods have been used to study nonlinear evolution equations, for analytic and numerical solutions. Examples of these methods are The sech method [2,10], Tanh-Sech method [10,35,36], Sin-Cosine method [33,34], F-expansion method [40,42,43], Generalized Kudryashov technique [12,39], Exp-function method [12,15,28,41], (G'/G) expansion method [12,27,32], Generalized (G'/G) expansion method [17,27,29], mapping method [24], darboux transformation method [14,22], Hirota bilinear method [21,39], Painlevé analysis [21], Rational (G'/G)-expansion method [8,16,26], among other methods.…”