Traveling Wave Solutions for Complex Space-Time Fractional Kundu-Eckhaus Equation

Mohammed Alabedalhadi, Mohammed Shqair (), Shrideh Al-Omari and Mohammed Al-Smadi
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Mohammed Alabedalhadi: Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
Mohammed Shqair: College of Science, Zarqa University, Zarqa 132222, Jordan
Shrideh Al-Omari: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Ajloun 26816, Jordan
Mohammed Al-Smadi: Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan

Mathematics, 2023, vol. 11, issue 2, 1-15

Abstract: In this work, the class of nonlinear complex fractional Kundu-Eckhaus equation is presented with a novel truncated M-fractional derivative. This model is significant and notable in quantum mechanics with good-natured physical characteristics. The motivation for this paper is to construct new solitary and kink wave solutions for the governing equation using the ansatz method. A complex-fractional transformation is applied to convert the fractional Kundu-Eckhaus equation into an ordinary differential equations system. The equilibria of the corresponding dynamical system will be presented to show the existence of traveling wave solutions for the governing model. A novel kink and solitary wave solutions of the governing model are realized by means of the proposed method. In order to gain insight into the underlying dynamics of the obtained solutions, some graphical representations are drawn. For more illustration, several numerical applications are given and analyzed graphically to demonstrate the ability and reliability of the method in dealing with various fractional engineering and physical problems.

Keywords: fractional Kundu-Eckhaus equation; solitary wave; kink wave; truncated M-fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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