A Study on the Exact Solutions of the Ramani Equation Using Lie Symmetry Analysis

被引：0

作者：

Agnus S. ^{[1
]}

Seshadri R. ^{[1
]}

Halder A.K. ^{[1
]}

Leach P.G.L. ^{[2
,3
]}

机构：

[1] Department of Mathematics, Pondicherry University, Puducherry, Kalapet

[2] School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban

[3] Institute for Systems Science, Durban University of Technology, Durban

来源：

International Journal of Applied and Computational Mathematics | 2024年 / 10卷 / 4期

基金：

新加坡国家研究基金会;

关键词：

Improved G[!sup]′[!/sup]G-expansion method; Lie symmetry; Ramani equation; Singularity analysis;

D O I：

10.1007/s40819-024-01758-w

中图分类号：

学科分类号：

摘要：

Shock waves propagating in a plasma medium are modelled by the sixth-order nonlinear Ramani equation. All possible closed-form solutions to the Ramani equation are derived through the holistic approach using the Lie symmetry method. This involves computing Lie point symmetries and the corresponding similarity reductions. However, certain symmetry-reduced ordinary differential equations possess no point symmetries. We investigate such equations through singularity analysis. Their solutions are obtained as right Painlevé series. In addition, we present the travelling-wave solutions of the original equation via the improved G′G-expansion method. The soliton-type, periodic, and hyperbolic graphs of the solutions which aid in comprehending the wave phenomenon is displayed. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

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