Symmetry analysis and invariant solutions of Riabouchinsky Proudman Johnson equation using optimal system of Lie subalgebras

Hussain, A.; Usman, M.; Zaman, F. D.; Eldin, Sayed M.

doi:10.1016/j.rinp.2023.106507

Cited by 21 publications

(5 citation statements)

References 18 publications

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“…A system of equations is created by inserting the necessary replacements to equations (21) and (25). After resolving this algebraic system, the subsequent parameters are obtained;…”

Section: Soliton-like Solutions Of the Tm Equation (4)mentioning

confidence: 99%

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Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets

Usman,

Hussain,

Zaman

2023

Phys. Scr.

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This article discusses the thermophoretic motion (TM) equation that is used to describe soliton-like thermophoresis of wrinkles in Graphene sheet based on the Korteweg-de Vries (KdV) equation. Wrinkle-like exact solutions are constructed using the Lie group method and modified auxiliary equation (MAE) approach. A graphic analysis of the solutions is done to show how various parameters may change the attributes of the solutions, such as breadth, amplitude, shape, and open direction.

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“…A system of equations is created by inserting the necessary replacements to equations (21) and (25). After resolving this algebraic system, the subsequent parameters are obtained;…”

Section: Soliton-like Solutions Of the Tm Equation (4)mentioning

confidence: 99%

“…Lie group methods [20][21][22][23][24][25][26][27][28] mainly deal with the nonlinear PDEs to furnish the exact solutions. This technique was initiated by Sophus Lie [29,30] and then followed by Ovsyannikov [31], Ibragimov [32], Bluman [33] and Hydon [34].…”

Section: Introductionmentioning

confidence: 99%

Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets

Usman,

Hussain,

Zaman

2023

Phys. Scr.

Self Cite

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“…In [42], authors did some analysis with optical soliton, group invariants and conservation laws of perturbed Fokas-Lenells equation. Some other work on the soliton solutions by different methods is done in [43][44][45][46][47]. In [48], authors have revealed the hole-like dark soliton, chirped-like dark soliton, and kink/antikink-like cuspon of the considered model.…”

Section: Introductionmentioning

confidence: 99%

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

Muhammad,

Abbas,

Hussain

et al. 2024

Phys. Scr.

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In this study, the new complex wave solutions of the perturbed Fokas-Lenells (p-FL) equation, which has applications in nonlinear optical fibers are obtained using a new extended direct algebraic method. This model represents recent electronic communications like Internet blogs, facebook communication and twitter comments. The obtained solutions are the different classes of traveling wave structures with singular solutions Type-I \& II, dark-singular, dark, and dark-bright solutions. Furthermore, stability conditions for the computed structures are reported. Also, graphical representations of some particular structures are shown by taking the specific values of the constants. The ordinary differential equation (ODE) obtained from a traveling wave transformation is converted into a dynamical system using Galilean transformation. The phase plane analysis is done for different values of the controlled parameters $d_1$ and $d_3$. A perturbation term is added to analyze the chaotic dynamics, and plots indicate that the system shows the chaotic dynamics. Also, sensitivity analysis shows that the system is sensitive to initial conditions. The conclusion is accounted for toward the end.

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“…Symmetry analysis [23][24][25][26][27][28] is a mathematical technique used to study and understand the symmetries inherent in equations or physical systems. Symmetries represent invariance properties under certain transformations.…”

Section: Introductionmentioning

confidence: 99%

Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra

Usman,

Hussain,

Zaman

et al. 2024

International Journal of Mathematics and Computer in Engineering

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This research focuses on the examination of nonlinear evolution equations, with a specific emphasis on the generalized coupled Zakharov-Kuznetsov (CZK) equations serving as a primary example. Given the wide application of classical Lie symmetry methods in this field, our study employs a Lie symmetry analysis to investigate the CZK equations, as detailed in this research. Our methodology involves the construction of a nine-dimensional optimal system by leveraging the fundamental elements of the Lie algebra. Subsequently, we apply similarity reductions to the equations using each subalgebra. The resulting invariant solutions find diverse applications within the realm of physics and can also be adapted to solve a broad range of related nonlinear evolution equations. We meticulously validate all these solutions through a straightforward verification process. To enhance our comprehension of the physical implications of these solutions, we employ Mathematica simulations to visually represent various solution scenarios. Additionally, to preserve conservation laws, we incorporate Ibragimov’s novel conservation law theorem as a crucial component of our analysis.

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Symmetry analysis and invariant solutions of Riabouchinsky Proudman Johnson equation using optimal system of Lie subalgebras

Cited by 21 publications

References 18 publications

Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets

Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra

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