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

Khalique, Chaudry Masood; Simbanefayi, Innocent

doi:10.1142/s0219887821501371

Cited by 4 publications

(2 citation statements)

References 26 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 new analytic approach and its application to new generalized Korteweg‐de Vries and modified Korteweg‐de Vries equations

Kumar,

Malik

2024

Math Methods in App Sciences

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The current study is important from two perspectives. Firstly, in this article, we suggest a novel analytical technique for creating the exact solutions to nonlinear partial differential equations (NLPDEs). In order to study the dynamical behaviors of various wave phenomena, we can construct the several exact solutions in the form of Jacobi elliptic solutions, hyperbolic solutions, trigonometric solutions, and exponential solutions by using this method. Secondly, we consider a more generalized form of the (2+1)‐dimensional Korteweg–de Vries (KdV) and modified Korteweg‐de Vries (mKdV) equations that plays an important role in describing the shallow water. We successfully extract several soliton solutions for the examined equation. By choosing the appropriate parameters, some graphs of the discovered solutions have been represented in the figures. Every obtained solution has been demonstrated to satisfy the corresponding equation. The findings demonstrate that the method can be applied to solve a number of nonlinear evolution equations. The new solutions and the paper's findings could improve our understanding of how the waves move through shallow water and open up new research avenues.

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The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods

2022

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

Cited by 4 publications

References 26 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

A new analytic approach and its application to new generalized Korteweg‐de Vries and modified Korteweg‐de Vries equations

The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods

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