Novel Approximate Analytical Solutions to the Nonplanar Modified Kawahara Equation and Modeling Nonlinear Structures in Electronegative Plasmas

In this investigation, the nonplanar (spherical and cylindrical) modified fifth-order Korteweg–de Vries (nmKdV5) equation, otherwise known as the nonplanar modified Kawahara equation (nmKE), is solved using the ansatz approach. Two general formulas for the semi-analytical symmetric approximations ar...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-01, Vol.15 (1), p.97
Main Authors: Alharbey, Rania A., Alrefae, Wasayf R., Malaikah, Hunida, Tag-Eldin, Elsayed, El-Tantawy, Samir A.
Format: Article
Language:English
Subjects:
ansatz method
Approximation
Cnoidal waves
electronegative plasmas
Electronegativity
Exact solutions
Investigations
Nonlinear phenomena
nonplanar modified Kawahara equation
nonplanar solitary and cnoidal waves
Physics
Plasma
Plasma physics
Plasmas (physics)
semi-analytical solutions
Solitary waves
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Summary:In this investigation, the nonplanar (spherical and cylindrical) modified fifth-order Korteweg–de Vries (nmKdV5) equation, otherwise known as the nonplanar modified Kawahara equation (nmKE), is solved using the ansatz approach. Two general formulas for the semi-analytical symmetric approximations are derived using the recommended methodology. Using the obtained approximations, the nonplanar modified Kawahara (mK) symmetric solitary waves (SWs) and cnoidal waves (CWs) are obtained. The fluid equations for the electronegative plasmas are reduced to the nmKE as a practical application for the obtained solutions. Using the obtained solutions, the characteristic features of both the cylindrical and spherical mK-SWs and -CWs are studied. All obtained solutions are compared with each other, and the maximum residual errors for these approximations are estimated. Numerous researchers that are interested in studying the complicated nonlinear phenomena in plasma physics can use the obtained approximations to interpret their experimental and observational findings.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15010097