Travelling wave solution of Dodd-Bullough-Mikhailov equation: a comparative study between Generalized Kudryashov and improved F-expansion methods

Abstract

We investigate the efficiency of Generalized Kudryashov and improved F-expansion methods in solving nonlinear partial differential equations. The Dodd-Bullough-Mikhailov equation is considered to implement these methods. Both methods allow us to construct a number of travelling wave solutions of the governing equation. However, the Generalized Kudryashov method is found more direct, effective and requires less tedious symbolic computations compared to the improved F-expansion method. Our analysis also reveal that the basic version of either of the methods could be effective enough to acquire the fundamental wave solutions of the governing equation.

New Soliton Solutions Arising in Some NLEEs

“…In this study, GKM, which is one of the solution methods of NLEEs, is discussed (Tuluce Demiray, 2020; Tuluce Demiray and Bayrakci, 2021;Pandır and Eren, 2021;Kaplan and Akbulut, 2021;Gurefe, 2020;Islam et al 2019). Firstly, the structure of the method is introduced.…”

On new analytical solutions of fractional systems in shallow water dynamics

“…It is very important to acquire the solutions of these equations used in these fields created by real-world problems. Among the powerful and effective methods used to achieve analytical solutions, the modified simple equation method [9], the generalized Kudryashov method [10], the improved F-expansion method [11], the new extended direct algebraic method [12], the (G /G)-expansion method [13], the ERF method [14], the first integral method [15], the modified trial equation method [16], the generalized exponential rational function method [17], the generalized bifurcation method [18], the modified extended tanh-function method [19], the sub-equation method [20], and so on. However, these methods need some specific definitions to be applied to equations containing fractional order derivatives.…”

Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations

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