Revised Lie Group Analysis of the Time Fractional (2+1)-Dimensional Zakharov-Kuznetsov (<i>q</i>, <i>p</i>, <i>r</i>) Equation
This article presents a comprehensive study of the (2+1)-dimensional Zakharov–Kuznetsov (ZK) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>q<...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/6/352 |
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| Summary: | This article presents a comprehensive study of the (2+1)-dimensional Zakharov–Kuznetsov (ZK) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>q</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> equation with time fractional derivativeUtilizing the fractional Lie group method, we derive several results, including the symmetries, similarity reductions and conservation laws for this equation. Our findings not only correct previous errors in the literature but also introduce new results, such as the Lie transformation group and optimal system for this model. The study provides a rigorous mathematical framework for analyzing this fundamental model, which describes nonlinear ion-acoustic wave evolution in magnetized plasmas. |
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| ISSN: | 2504-3110 |