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Invariant analysis of the multidimensional Martinez Alonso–Shabat equation

  • Naseem Abbas EMAIL logo , Akhtar Hussain , Muhammad Waseem Akram , Shah Muhammad and Mohammad Shuaib
Published/Copyright: August 19, 2024
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 79 Issue 10

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.

Keywords: symmetries; optimal system; symmetry reductions; group-invariant solutions; conservation laws; multiplier method
Corresponding author: Naseem Abbas, Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan, E-mail: 

Acknowledgments

This research is funded by “Researchers Supporting Project number (RSPD2024R733),” King Saud University, Riyadh, Saudi Arabia.

  1. Research ethics: Not applicable.

  2. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  3. Competing interests: The authors declare no conflicts of interest regarding this article.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

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Received: 2024-05-19
Accepted: 2024-07-30
Published Online: 2024-08-19
Published in Print: 2024-10-28

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Optical Physics
  3. Research on adaptive optics technology based on phase contrast Gerchberg Saxton algorithm
  4. Dynamical Systems & Nonlinear Phenomenas
  5. Free vibration analyses of 3D printed plates with different geometric fillings: experimental testing and numerical simulations
  6. Dynamical investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative
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https://doi.org/10.1515/zna-2024-0115
Keywords for this article
symmetries; optimal system; symmetry reductions; group-invariant solutions; conservation laws; multiplier method

Articles in the same Issue

  1. Frontmatter
  2. Atomic, Molecular & Optical Physics
  3. Research on adaptive optics technology based on phase contrast Gerchberg Saxton algorithm
  4. Dynamical Systems & Nonlinear Phenomenas
  5. Free vibration analyses of 3D printed plates with different geometric fillings: experimental testing and numerical simulations
  6. Dynamical investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative
  7. Invariant analysis of the multidimensional Martinez Alonso–Shabat equation
  8. Solid State Physics & Materials Science
  9. Computation Legendre moments using image analysis technique
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