• Invariance analysis, optimal system and conservation laws of $(2 + 1)$-dimensional non-linear Vakhnenko equation

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/095/0008

• # Keywords

Vakhnenko equation; Lie group of transformation; infinitesimal generator; adjoint equations; optimal system; conservation laws; invariant solutions.

• # Abstract

In this article, we study a $(2 + 1)$-dimensional non-linear Vakhnenko equation which appears in a relaxing high rate active barothropic medium. The Lie symmetry analysis is applied to study the solution of $(2+1)$-dimensional Vakhnenko equation and also used to find the optimal system of one-dimensional Lie subalgebra. The two-dimensional non-linear Vakhnenko equation is reduced to various ordinary differential equations by applying similarity transformation method, and solving these reduced ordinary differential equations, we find invariant solutions of $(2 + 1)$-dimensional Vakhnenko equation. Moreover, the adjoint equation of the Vakhnenko equation and its conservation laws are also obtained, which can be used for mathematical analysis.

• # Author Affiliations

1. Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, India

• # Pramana – Journal of Physics

Volume 96, 2022
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• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019