Invariant analysis of the multidimensional Martinez Alonso–Shabat equation-Reference-Cited by-同舟云学术

Invariant analysis of the multidimensional Martinez Alonso–Shabat equation

Published:2024-08-19 Issue: Volume: Page:
ISSN:0932-0784
Container-title:Zeitschrift für Naturforschung A
language:en
Short-container-title:

Author:

Abbas Naseem¹,Hussain Akhtar²,Waseem Akram Muhammad³,Muhammad Shah⁴,Shuaib Mohammad⁵

Affiliation:

1. Department of Mathematics , 66757 Quaid-i-Azam University , Islamabad 45320 , Pakistan

2. Abdus Salam School of Mathematical Sciences , Government College University , Lahore 54600 , Pakistan

3. Department of Mathematics and Computer Science , University of Calabria , Rende , CS 87036 , Italy

4. Department of Mathematics, College of Science , King Saud University , P.O. Box 2455 , Riyadh 11451 , Saudi Arabia

5. Department of Mathematics , Lovely Professional University , Phagwara , Punjab , India

Abstract

Abstract This present study is concerned with the group-invariant solutions of the (3 + 1)-dimensional Martinez Alonso–Shabat equation by using the Lie symmetry method. The Lie transformation technique is used to deduce the infinitesimals, Lie symmetry operators, commutation relations, and symmetry reductions. The optimal system for the obtained Lie symmetry algebra is obtained by using the concept of the adjoint map. As for now, the considered model equation is converted into nonlinear ordinary differential equations (ODEs) in two cases in the symmetry reductions. The exact closed-form solutions are obtained by applying constraint conditions on the symmetry generators. Due to the presence of arbitrary functional parameters, these group-invariant solutions are displayed based on suitable numerical simulations. The conservation laws are obtained by using the multiplier method. The conclusion is accounted for toward the end.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/zna-2024-0115/pdf

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