Abstract
Abstract This article aims to address the exact solution of the prestigious partial differential equation, namely, a double dispersive equation. Here, we are obtaining some new traveling wave solutions of the double dispersive equation with the more general mathematical technique, which is a direct algebraic extended method. This proposed technique is more general and integrated. The obtained solutions contain dark, bright, dark–bright, singular, periodic, kink, and rational function solutions. More illustration of traveling wave solutions of the double dispersive equation is given by plotting the two- and three-dimensional graphs with the suitable selection of parameters. This graphical presentation of solutions identifies the pattern of wave propagation. The acquired consequences are new and may play a significant role to examine the physical phenomena of wave propagation, where this model is used.
Highlights
This article aims to address the exact solution of the prestigious partial differential equation, namely, a double dispersive equation
The used scheme is not much as compared to our used technique, that is why some special types of solitons solutions missed such as rational solution, logarithmic solutions, kink-type solution, and many more. To fulfill this curiosity, the direct extended algebraic method has been operated on the double dispersive equation and acquired some novel results that did not exist in the literature
We have investigated the traveling wave solutions and observed that the acquired solutions have satisfied the governing wave propagation model
Summary
We are obtaining some new traveling wave solutions of the double dispersive equation with the more general mathematical technique, which is a direct algebraic extended method. The exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr non-linearity form are derived utilizing the extended sinh-Gordon expansion and Jacobielliptic function method [27]. The used scheme is not much as compared to our used technique, that is why some special types of solitons solutions missed such as rational solution, logarithmic solutions, kink-type solution, and many more To fulfill this curiosity, the direct extended algebraic method has been operated on the double dispersive equation and acquired some novel results that did not exist in the literature.
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