"Exact Soliton Solutions for Conformable Fractional Four-Wave Interacti" by Adeeb G. Talafha, Sahar M. Alqaraleh et al.

Progress in Fractional Differentiation & Applications

Article Title

Exact Soliton Solutions for Conformable Fractional Four-Wave Interaction Equations Using Ansatz Method

Authors

Adeeb G. Talafha, Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal University, Ma’an, JordanFollow
Sahar M. Alqaraleh, Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal University, Ma’an, JordanFollow
Mohammed Al-Smadi, Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan\\ Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAEFollow
Samir Hadid, Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAEFollow
Shaher Momani, Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE\\ Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanFollow

Author Country (or Countries)

Jordan

Abstract

In this paper, the conformable time-fractional derivative of order α ∈ (0,1] is considered, instead of the classical time derivative for α = 1, in view of the Lax-pair operator that leads to a fractional nonlinear evolution system of four-wave-interaction-equations (4-WIEs). The resulted system is then solved by an ansatz contains tan and secant hyperbolic functions with complex coefficients. A systematic steps are introduced to obtain a general form of exact soliton solutions for the resulted system in (1+1) one spatial and one temporal dimensions. We showed that the obtained solutions could be modified to represent solutions of a similar system but in (2+1) two spatial and one temporal dimensions too. In fact, our suggested ansatz can be used to obtain exact soliton solutions for fractional N-wave-interaction-equations (N-WIEs) in one or more spatial dimensions for N greater than or equal to four. Eventually, some numerical examples are stated with 3D graphs to give a better understanding of the behavior of the soliton waves while the interaction is turned on.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080408

Recommended Citation

G. Talafha, Adeeb; M. Alqaraleh, Sahar; Al-Smadi, Mohammed; Hadid, Samir; and Momani, Shaher (2022) "Exact Soliton Solutions for Conformable Fractional Four-Wave Interaction Equations Using Ansatz Method," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 4, Article 8.
DOI: http://dx.doi.org/10.18576/pfda/080408
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss4/8

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