EXACT SOLITON SOLUTIONS FOR CONFORMABLE FRACTIONAL SIX WAVE INTERACTION EQUATIONS BY THE ANSATZ METHOD

Sahar M. Alqaraleh, Adeeb G. Talafha, Shaher Momani, Shrideh Al-Omari and Mohammed Al-Smadi
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Sahar M. Alqaraleh: Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal University, Ma’an, Jordan
Adeeb G. Talafha: Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal University, Ma’an, Jordan
Shaher Momani: ��Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 20550, UAE‡Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan
Shrideh Al-Omari: �Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan
Mohammed Al-Smadi: ��Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 20550, UAE¶Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-16

Abstract: In this paper, a conformable fractional time derivative of order α ∈ (0, 1] is considered in view of the Lax-pair of nonlinear operators to derive a fractional nonlinear evolution system of partial differential equations, called the Fractional-Six-Wave-Interaction-Equations, which is derived in terms of one temporal plus one and two spatial dimensions. Further, an ansatz consisting of linear combinations of hyperbolic functions with complex coefficients is utilized to obtain an infinite set of exact soliton solutions for this system. Certain numerical examples are introduced to show the effectiveness of the ansatz method in obtaining exact solutions for similar systems of nonlinear evolution equations.

Keywords: Fractional Derivative; Six-Wave Equations; Solitons; Ansatz Method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401430

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