An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation

Simbanefayi, Innocent; Khalique, Chaudry Masood

doi:10.1515/phys-2020-0193

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…We adopt power series technique [45][46][47] to secure a solution of the complicated NODE (2.47) having forty-four terms which involves a quite lengthy calculations. We begin this process by assuming a series solution of a formal structure…”

Section: Steady-state Power Series Solution Of (18) In Explicit Formmentioning

confidence: 99%

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An optimal System of Lie Subalgebras and Group-Invariant Solutions with Conserved Currents of a (3+1)-D Fifth-Order Nonlinear Model I with Applications in Electrical Electronics, Chemical Engineering and Pharmacy

Adeyemo

Khalique

2023

J Nonlinear Math Phys

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Higher-dimensional nonlinear integrable partial differential equations are significant as they often describe diverse phenomena in nonlinear systems like laser radiations in a plasma, optical pulses in the glass fibres, fluid mechanics, radio waves in the ion sphere, condensed matter and electromagnetics. This article shows an analytical investigation of a (3+1)-dimensional fifth-order nonlinear model with KdV forming its main part. Lie group analysis of the model is performed through which its infinitesimal generators are obtained. These generators are engaged in the construction of an optimal system of Lie subalgebra in one dimension. Moreover, members of the system secured are utilized in reducing the underlying model to ordinary differential equations (ODEs) for possible exact solutions. In consequence, we achieve various functions, ranging from trigonometric, logarithmic, rational, to hyperbolic. In addition, the results found constitute diverse solitonic solutions such as complex, topological kink and anti-kink, trigonometric and bright. We utilize the power series technique to obtain a series solution of the most complicated ordinary differential equation with forty-four terms. In addition, we reveal the dynamics of these solutions via graphical depictions. In the end, we constructed conserved currents of the underlying equation through the use of the multiplier technique. Further, we utilize the optimal system of the underlying model to derive more conserved vectors using Ibragimov’s theorem for conservation laws.

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Section: Steady-state Power Series Solution Of (18) In Explicit Formmentioning

confidence: 99%

“…. ; T 4 ) for each of the terms in the equation which involves some lengthy calculations and by expanding the result, we have a more simplified structure given as (see [45][46][47])…”

Section: Appendix-detailed Computations Of the Steady-state Power Ser...mentioning

confidence: 99%

An optimal System of Lie Subalgebras and Group-Invariant Solutions with Conserved Currents of a (3+1)-D Fifth-Order Nonlinear Model I with Applications in Electrical Electronics, Chemical Engineering and Pharmacy

Adeyemo

Khalique

2023

J Nonlinear Math Phys

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Conservation laws, classical symmetries and exact solutions of a (1 + 1)-dimensional fifth-order integrable equation

Khalique

Simbanefayi

2021

Int. J. Geom. Methods Mod. Phys.

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In this paper, we present a study of a fifth-order nonlinear partial differential equation, which was recently introduced in the literature. This equation can be used as a model for bidirectional water waves propagating in a shallow medium. Using elements of an optimal system of one-dimensional subalgebras, we perform similarity reductions culminating in analytic solutions. Rational, hyperbolic, power series and elliptic solutions are obtained. Furthermore, by using the multiple exponential function method we obtain one and two soliton solutions. Finally, local and low-order conserved quantities are derived by enlisting the multiplier approach.

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An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation

Cited by 2 publications

References 27 publications

An optimal System of Lie Subalgebras and Group-Invariant Solutions with Conserved Currents of a (3+1)-D Fifth-Order Nonlinear Model I with Applications in Electrical Electronics, Chemical Engineering and Pharmacy

An optimal System of Lie Subalgebras and Group-Invariant Solutions with Conserved Currents of a (3+1)-D Fifth-Order Nonlinear Model I with Applications in Electrical Electronics, Chemical Engineering and Pharmacy

Conservation laws, classical symmetries and exact solutions of a (1 + 1)-dimensional fifth-order integrable equation

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