Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type system

Khalique, Chaudry Masood; Simbanefayi, Innocent

doi:10.1016/j.jare.2020.10.002

Cited by 13 publications

(3 citation statements)

References 42 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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“…A classification of conservation laws of a generalized quasilinear KdV equation was provided in [29] too. Moreover, a (1 + 1)-dimensional coupled modified KdV-type system was studied in [30], constructing its conservation laws also using the multiplier method.…”

Section: Introductionmentioning

confidence: 99%

Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation

Márquez

Bruzón

2021

Mathematics

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This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie’s symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partial differential equation to some ordinary differential equations, by using the symmetries. Therefore, new analytical solutions are found from the ordinary differential equations. Finally, we derive low-order conservation laws, depending on the form of the damping and source terms, and discuss their physical meaning.

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Higher-dimensional soliton structures of a variable-coefficient Gross–Pitaevskii equation with the partially nonlocal nonlinearity under a harmonic potential

et al. 2022

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Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type system

Abstract: Graphical abstract

Cited by 13 publications

References 42 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

Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation

Higher-dimensional soliton structures of a variable-coefficient Gross–Pitaevskii equation with the partially nonlocal nonlinearity under a harmonic potential

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