Investigating analytical and numerical techniques for the $$(2+1) {\mathfrak {q}}$$-deformed equation

Ali, Khalid K.; Mohamed, Mohamed S.; Alharbi, Weam G.

doi:10.1007/s00033-024-02313-9

Z. Angew. Math. Phys.

2024

DOI: 10.1007/s00033-024-02313-9

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Investigating analytical and numerical techniques for the $$(2+1) {\mathfrak {q}}$$-deformed equation

Khalid K. Ali,

Mohamed S. Mohamed,

Weam G. Alharbi

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2024

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Cited by 2 publications

References 27 publications

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Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

Ali

2024

Z. Angew. Math. Phys.

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In this study, we investigate the (3+1) q-deformed tanh-Gordon equation due to its importance in the context of mathematical physics. It describes solitonic solutions in quantum field theory; it can sometimes be used in condensed matter physics to describe interactions between particles in magnetic materials or superconductors; it can model light propagation in nonlinear optical fibers or photonic crystals where the refractive index has a q-deformed structure; and it also can be applied in studying shock waves, turbulence and rogue waves where the deformation introduces corrections to classical wave phenomena. Utilizing the $$(\frac{{\mathfrak {G}}^{\prime }}{\omega {\mathfrak {G}}^{\prime }+{\mathfrak {G}}+r})$$ ( G ′ ω G ′ + G + r ) -expansion technique, we derive novel analytical solutions that enhance our understanding of the underlying dynamics. Additionally, we employ a finite element method (extended cubic B-spline method) to validate our analytical findings and explore the behavior of the q-deformed equation under different parameter regimes. Our results demonstrate the versatility of the q-deformed framework in generating rich optical phenomena, paving the way for future research in both theoretical and applied physics.

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Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

Ali

2024

Z. Angew. Math. Phys.

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Fractional analysis of the (2+1) $$\mathfrak {q}$$-deformed tanh-Gordon equation with optimal homotopy with $$\mathbb {J}$$-transform

Ali,

Mohamed,

Maneea

2024

Z. Angew. Math. Phys.

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Investigating analytical and numerical techniques for the $$(2+1) {\mathfrak {q}}$$-deformed equation

Cited by 2 publications

References 27 publications

Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

Fractional analysis of the (2+1) $$\mathfrak {q}$$-deformed tanh-Gordon equation with optimal homotopy with $$\mathbb {J}$$-transform

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