Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G'/G,1/G) -Expansion Method

Abstract

In this work, we investigate solitary wave solutions of the coupled Konno-Oono equation with the aid of the functional variable method (FVM) and the two variables !We obtain solitary wave solutions in form of trigonometric function, hyperbolic function and rational function solutions. We also draw two and three-dimensional graphics for some solutions with help of Mathematica 7.

Dynamical Behaviour of Conformable Time-Fractional Coupled Konno-Oono Equation in Magnetic Field

“…In [23], the tanh-function method and extended tanh-function method have been applied to construct soliton solutions for system (3). Additional methods have been forced such as a new generalized (G′/G)−expansion method [24], the modified exp(−Ω(ξ))− expansion function method [25], the sine-Gordon expansion method [26], the external trial equation method [27], the generalized exp-function method [28], a modified extended exp-function method [29], the extended simplest equation method [30], the extended Jacobian elliptic function expansion method [31], the functional variable and the two variables (G ′ /G, 1/G)− expansion methods [32], and a new extended direct algebraic method [33]. Recently, some techniques have been imposed such as a generalized (G ′ /G)− expansion method for stochastic Konno-Oono equation that is forced by multiplicative noise term [34] and a unified solver with the aid of probability function distributions [35], for more details about wave solutions for stochastic PDE (see, e.g., [36][37][38]).…”

Construction of Different Types of Traveling Wave Solutions of the Relativistic Wave Equation Associated with the Schrödinger Equation

“…So the discussion of NPDEs exact solutions in the nonlinear sciences is very important. Over the past few years, many researchers have used this beneficial method extensively, for example, the Jacobi elliptic expansion method [1], modified Kudryashov method [2,3], the tanh method [4], sub-equation analytical method [5], the inverse scattering method [6], the first integral method [7,8], the extended tanh-function method [9,10], the Hirota's direct method [11], the auxiliary equation method [12], improved Bernoulli sub-equation function method [13], expansion method [14], (G /G, 1/G)-expansion method [15,16,17], generalized exponential rational function method [18,19,24], Sinh-Gordon function method [20], Sine-Gordon expansion method [21], Bernoulli sub-equation method [22], (G /G)-expansion method [23]. The equation of the Eckhaus is as follows [25]:…”

Simulation of Wave Solutions of a Mathematical Model Representing Communication Signals

“…The solutions obtained as a result of applying these techniques allow commenting on the behavior of mathematical models. Some of them are the (𝐺 ′ 𝐺 ⁄ )-expansion technique and its modifications (Wang et al, 2008;Naher, 2012;Naher and Abdullah, 2013;Akbar et al, 2016;Duran, 2020;, the (1/G')expansion method , sine-Gordon expansion method and (𝑚 + 𝐺 ′ 𝐺) ⁄ -expansion method (Ismael et al, 2020), the improved Bernoulli sub-equation function method Duran et al, 2021), the Riccati-Bernoulli sub-ODE method (Yang et al, 2015), the exp(−ϕ(ξ))-expansion method and its improved forms (Misirli and Gurefe, 2011;Arshed et al, 2019;Chen et al, 2019;Yel et al, 2019;Baskonus, 2021;, the generalized Kudryashov method (Demiray et al, 2015;Mahmud et al, 2017;Rahman et al, 2019), the new function method (Aktürk et al, 2017), the Hirota's bilinear transformation (Hietarinta, 2005), the Backlund transformation method (Hirota and Satsuma, 1977;Lu et al, 2006), rational sine-cosine method (Marwan et al 2011;Qawasmeh and Alquran, 2014) the tanh method and its various extension (Fan, 2000;Elwakil et al, 2005;Yang and Hon, 2006), the tanh-coth expansion method (Wazwaz, 2007a(Wazwaz, , 2007bParkes, 2010), the homotopy perturbation method (He, 2006a(He, , 2006b(He, , 2008Biazar et al, 2009), the simplified Hirota's method (Wazwaz, 2016), the extended sinh-Gordon equation expansion method (Kumar et al, 2018;…”