Exploring Families of Solitary Wave Solutions for the Fractional Coupled Higgs System Using Modified Extended Direct Algebraic Method

In this paper, we suggest the modified Extended Direct Algebraic Method (mEDAM) to examine the existence and dynamics of solitary wave solutions in the context of the fractional coupled Higgs system, with Caputo’s fractional derivatives. The method begins with the formulation of nonlinear differenti...

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Bibliographic Details
Published in:Fractal and fractional 2023-09, Vol.7 (9), p.653
Main Authors: Bilal, Muhammad, Iqbal, Javed, Ali, Rashid, Awwad, Fuad A., Ismail, Emad A. A.
Format: Article
Language:English
Subjects:
Algebra
Differential equations
Family
Fourier transforms
FPDEs
kink waves
Laplace transforms
lump waves
Mathematical analysis
mEDAM
Methods
NODE
Nonlinear differential equations
Partial differential equations
Quantum field theory
Solitary waves
Traveling waves
variable transformation
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Summary:In this paper, we suggest the modified Extended Direct Algebraic Method (mEDAM) to examine the existence and dynamics of solitary wave solutions in the context of the fractional coupled Higgs system, with Caputo’s fractional derivatives. The method begins with the formulation of nonlinear differential equations using a fractional complex transformation, followed by the derivation of solitary wave solutions. Two-dimensional, Three-dimensional and contour graphs are used to investigate the behavior of traveling wave solutions. The research reveals many families of solitary wave solutions as well as their deep interrelationships and dynamics. These discoveries add to a better understanding of the dynamics of the fractionally coupled Higgs system and have potential applications in areas that use nonlinear Fractional Partial Differential Equations (FPDEs).
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7090653