Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations

Paliathanasis, Andronikos

doi:10.2989/16073606.2021.1928323

Quaestiones Mathematicae

2021

DOI: 10.2989/16073606.2021.1928323

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Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations

Andronikos Paliathanasis

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Cited by 2 publications

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Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations

Paliathanasis

2023

Mod. Phys. Lett. A

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We present a complete algebraic classification of the Lie symmetries for generalized Zoomeron equations. For the generalized [Formula: see text] and [Formula: see text] Zoomeron equations we solve the Lie symmetry conditions in order to constrain the free functions of the equations. We find that the differential equations of our consideration admit the same number of Lie symmetries with the non-generalized equations. The admitted Lie symmetries form the Lie algebras [Formula: see text], [Formula: see text] for the [Formula: see text] generalized Zoomeron equation, and the [Formula: see text], [Formula: see text] in the case of the [Formula: see text] generalized Zoomeron equation. The one-dimensional optimal system is constructed for the two equations and similarity solutions are derived. The similarity transformation led to the derivation of kink solutions. Indeed, the similarity exact solutions determined in this work are asymptotic solutions near the singular behavior of the kink behavior.

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Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations

Paliathanasis

2023

Mod. Phys. Lett. A

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Reduce-Order Modeling and Higher Order Numerical Solutions for Unsteady Flow and Heat Transfer in Boundary Layer with Internal Heating

et al. 2022

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We obtain similarity transformations to reduce a system of partial differential equations representing the unsteady fluid flow and heat transfer in a boundary layer with heat generation/absorption using Lie symmetry algebra. There exist seven Lie symmetries for this system of differential equations having three independent and three dependent variables. We use these Lie symmetries for the reduced-order modeling of the flow equations by constructing invariants corresponding to linear combinations of these Lie point symmetries. This procedure reduces one independent variable of the concerned fluid flow model when applied once. Double reductions are achieved by employing invariants twice that lead to ordinary differential equations with one independent and two dependent variables. Similarity transformations are constructed using these two sets of derived invariants corresponding to linear combinations of the Lie point symmetries. These similarity transformations have not been obtained earlier for this flow model. Moreover, the corresponding reduced systems of ordinary differential equations are different from those which exist in the literature for fluid flow and heat transfer that we have been dealing with. We obtain multiple similarity transformations which lead us to new classes of systems of ordinary differential equations. Accurate numerical solutions of these systems are obtained using the combination of an adaptive fourth-order Runge–Kutta method and shooting procedure. Effects of variation of unsteadiness parameter, Prandtl number and heat generation/absorption on fluid velocity, skin friction, surface temperature and heat flux are studied and presented with the help of tables and figures.

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Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations

Cited by 2 publications

References 47 publications

Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations

Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations

Reduce-Order Modeling and Higher Order Numerical Solutions for Unsteady Flow and Heat Transfer in Boundary Layer with Internal Heating

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