Symmetry analysis and closed-form invariant solutions of the nonlinear wave equations in elasticity using optimal system of Lie subalgebra

Hussain, A.; Usman, M.; Al-Sinan, Bushra R.; Osman, Waleed M.; Ibrahim, Tarek F.

doi:10.1016/j.cjph.2023.02.011

Cited by 31 publications

(12 citation statements)

References 11 publications

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“…Now we follow the soliton solutions of the TM equation (4) by using ODE (22). The balancing index obtained from equation ( 22) is n = 1.…”

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

confidence: 99%

“…A system of equations is created by inserting the necessary replacements to equations (22) and (25). After resolving this algebraic system, the subsequent parameters are obtained; Set 1…”

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%

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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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“…Now we follow the soliton solutions of the TM equation (4) by using ODE (22). The balancing index obtained from equation ( 22) is n = 1.…”

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

confidence: 99%

“…A system of equations is created by inserting the necessary replacements to equations (22) and (25). After resolving this algebraic system, the subsequent parameters are obtained; Set 1…”

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

confidence: 99%

See 1 more Smart Citation

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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“…The objective of this research is to showcase results and recent developments in the theory of evolution equations, encompassing both theoretical and practical aspects. Many researchers and mathematicians have suggested a variety of efficient methods 1 – 6 for finding exact solutions of nonlinear (NPDEs), such as Hirota’s bilinear method 7 , tanh function method 8 , the inverse scattering technique 9 , the Bäcklund transformation method 10 , modified variational iteration method 11 , the multiple exp-function approaches 12 , the Darboux transformation approach 13 , the Lie symmetry analysis 14 – 16 , the -expansion approach 17 , the Kudryashov technique 18 and the Jacobi elliptic technique 19 – 21 .…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system

Hussain,

Parveen,

Younis

et al. 2024

Sci Rep

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Utilizing nonlinear evolution equations (NEEs) is common practice to establish the fundamental assumptions underlying natural phenomena. This paper examines the weakly dispersed non-linear waves in mathematical physics represented by the Konopelchenko-Dubrovsky (KD) equations. The $$(G^\prime /G^2)$$ ( G ′ / G 2 ) -expansion method is used to analyze the model under consideration. Using symbolic computations, the $$(G^\prime /G^2)$$ ( G ′ / G 2 ) -expansion method is used to produce solitary waves and soliton solutions to the $$(2+1)$$ ( 2 + 1 ) -dimensional KD model in terms of trigonometric, hyperbolic, and rational functions. Mathematica simulations are displayed using two, three, and density plots to demonstrate the obtained solitary wave solutions’ behavior. These proposed solutions have not been documented in the existing literature.

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Symmetry analysis and closed-form invariant solutions of the nonlinear wave equations in elasticity using optimal system of Lie subalgebra

Cited by 31 publications

References 11 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

Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system

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