The Application of the Functional Variable Method for Solving the Loaded Non-linear Evaluation Equations - Babajanov, Bazar; Abdikarimov, Fakhriddin (Frontiers in Applied Mathematics and Statistics, 2022)
In this article, we construct exact travelling wave solutions of the loaded Korteweg-de Vries, the loaded modified Korteweg-de Vries and the loaded Gardner equation by the functional variable method. The operation of this method is reliable and efficient, providing precise individual and periodic wave solutions. All solutions of these equations were checked and three-dimensional graphs of the solutions obtained using the Matlab program were drawn. We get some traveler wave solutions represented by hyperbolic functions and trigonometric functions. Graphical representations of some of the solutions obtained are shown to better understand their physical properties, including bell-shaped solitary wave solutions, single-soliton solutions, and kink-type solitary wave solutions. Our results show that this method is a very efficient and simple method of formulating precisely moving wave solutions of nonlinear wave equations that emerge in mathematical physics and engineering.