Analysis of analytical solutions of fractional Date-Jimbo-Kashiwara-Miwa equation. (English) Zbl 1522.35146
Summary: In this study, the authors solved the \((2 + 1)\)-dimensional fractional Date-Jimbo-Kashiwara-Miwa equation for nonlinear dispersive waves in an inhomogeneous medium, which is an extension of the Kadomtsev-Petviashvili hierarchy. A powerful analytical technique, the new auxiliary equation method, is employed to develop the class of soliton solutions to the considered equation which contains dark, bright, and periodic wave solutions. A comparative analysis is done by using two fractional derivatives, namely, \(\beta\) and Atangana-Baleanu. While using this technique, the nonlinear ordinary differential equation in integer order is formed using chain rule from the fractional Date-Jimbo-Kashiwara-Miwa equation. There is no more a requirement to perform any normalization or discretization because of the chain rule. These obtained results are graphically portrayed such as \(3D\) and \(2D\) using suitable parametric values. The exact solutions to this equation are necessary to comprehend wave behavior in physical models. Moreover, a sensitive analysis to the fractional dynamical system is performed and graphically shown the behavior on initial conditions.
MSC:
| 35C08 | Soliton solutions |
| 35C07 | Traveling wave solutions |
| 35R11 | Fractional partial differential equations |
Keywords:
fractional Date-Jimbo-Kashiwara-Miwa equation; solitary wave solutions; analytical technique; fractional operators; sensitive analysisReferences:
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