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Search Results (3)

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Keywords = q-deformed Sinh-Gordon equation

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19 pages, 1216 KiB  
Article
The Analysis of Bifurcation, Quasi-Periodic and Solitons Patterns to the New Form of the Generalized q-Deformed Sinh-Gordon Equation
by Syeda Sarwat Kazmi, Adil Jhangeer, Nauman Raza, Haifa I. Alrebdi, Abdel-Haleem Abdel-Aty and Hichem Eleuch
Symmetry 2023, 15(7), 1324; https://doi.org/10.3390/sym15071324 - 28 Jun 2023
Cited by 65 | Viewed by 2398
Abstract
In this manuscript, a new form of the generalized q-deformed Sinh-Gordon equation is investigated which could model physical systems with broken symmetries and to incorporate phenomena involving amplification or dissipation. The proposed model is explored based on the Lie symmetry approach. Using [...] Read more.
In this manuscript, a new form of the generalized q-deformed Sinh-Gordon equation is investigated which could model physical systems with broken symmetries and to incorporate phenomena involving amplification or dissipation. The proposed model is explored based on the Lie symmetry approach. Using similarity reduction, the partial differential equation is transformed into an ordinary differential equation. By employing the generalized auxiliary equation approach, precise results for the derived equation are obtained. The solutions are graphically depicted as 3D, 2D, and contour plots. Furthermore, the qualitative analysis of the considered model is investigated by employing the concepts of bifurcation and chaos. The phase profiles are displayed for different sets of the parameters. Additionally, by applying an external periodic strength, quasi-periodic and chaotic behaviors are documented. Various tools for detecting chaos are discussed, including 3D and 2D phase patterns, time series, and Poincaré maps. Additionally, a sensitivity analysis is conducted for various initial conditions. The obtained findings are unique and indicate the viability and efficacy of the suggested strategies for evaluating soliton solutions and phase illustrations for various nonlinear models. Full article
(This article belongs to the Special Issue Partial Differential Equations and Their Applications in Nonlinear Optics)
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11 pages, 2591 KiB  
Article
Analytical Solutions for a New Form of the Generalized q-Deformed Sinh–Gordon Equation: ∂2u∂z∂ζ=eαu[sinhq(uγ)]p−δ
by Khalid K. Ali, Haifa I. Alrebdi, Norah A. M. Alsaif, Abdel-Haleem Abdel-Aty and Hichem Eleuch
Symmetry 2023, 15(2), 470; https://doi.org/10.3390/sym15020470 - 10 Feb 2023
Cited by 11 | Viewed by 1934
Abstract
In this article, a new version of the generalized q-deformed Sinh–Gordon equation is presented, and analytical solutions are developed for specific parameter sets using those equations. There is a possibility that the new equation can be used to model physical systems that [...] Read more.
In this article, a new version of the generalized q-deformed Sinh–Gordon equation is presented, and analytical solutions are developed for specific parameter sets using those equations. There is a possibility that the new equation can be used to model physical systems that have broken symmetries and include also effects related to amplification or dissipation. In addition, we have include some illustrations that depict the varied patterns of soliton propagation. Full article
(This article belongs to the Special Issue Symmetries in Differential Equation and Application)
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12 pages, 798 KiB  
Article
A Variety of New Explicit Analytical Soliton Solutions of q-Deformed Sinh-Gordon in (2+1) Dimensions
by Haifa I. Alrebdi, Nauman Raza, Saima Arshed, Asma Rashid Butt, Abdel-Haleem Abdel-Aty, Clemente Cesarano and Hichem Eleuch
Symmetry 2022, 14(11), 2425; https://doi.org/10.3390/sym14112425 - 16 Nov 2022
Cited by 14 | Viewed by 2033
Abstract
In this paper, the (2+1)-dimensional q-deformed Sinh-Gordon model has been investigated via (G′G,1G)-expansion and Sine-Gordon-expansion methods. These techniques successfully retrieve trigonometric as well as hyperbolic solutions, along necessary restricted conditions applied on parameters. In addition [...] Read more.
In this paper, the (2+1)-dimensional q-deformed Sinh-Gordon model has been investigated via (G′G,1G)-expansion and Sine-Gordon-expansion methods. These techniques successfully retrieve trigonometric as well as hyperbolic solutions, along necessary restricted conditions applied on parameters. In addition to these solutions, dark solitons and complexiton solutions have also been obtained. The proposed equation expands the possibilities for modeling physical systems in which symmetry is broken. The obtained solutions are graphically illustrated. A Painlevé analysis for the proposed model has also been discussed in this paper. Full article
(This article belongs to the Special Issue Fractional Dynamic Inequalities with Numerical Techniques and Its Application to Arbitrary Time Scales)
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