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Optimal systems, conservation laws, and invariance analysis of the (2 + 1) extended Boiti-Leon-Manna-Pempinelli equation via the lie symmetry approach

Akshita Bhardwaj, Shalini Yadav, Muhammad Junaid-U-Rehman, Rajan Arora

Abstract

Lie symmetry analysis has been applied to the extended Boiti-Leon-Manna-Pempinelli (eBLMP) equation. This system illustrates the exchange of information between two waves with distinct dispersion characteristics. The optimal system of the corresponding Lie algebra has been constructed. The equation considered has been reduced into a simpler form for the computation of analytical solutions. The novelty of this research is the optimal system of subalgebras in one dimension using the adjoint action approach. To analyze and understand the eBLMP more clearly, graphs have been plotted. We have also found conservation laws

Optimal systems, conservation laws, and invariance analysis of the (2 + 1) extended Boiti-Leon-Manna-Pempinelli equation via the lie symmetry approach

Abstract

Lie symmetry analysis has been applied to the extended Boiti-Leon-Manna-Pempinelli (eBLMP) equation. This system illustrates the exchange of information between two waves with distinct dispersion characteristics. The optimal system of the corresponding Lie algebra has been constructed. The equation considered has been reduced into a simpler form for the computation of analytical solutions. The novelty of this research is the optimal system of subalgebras in one dimension using the adjoint action approach. To analyze and understand the eBLMP more clearly, graphs have been plotted. We have also found conservation laws

Paper Structure

This paper contains 17 sections, 1 theorem, 73 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Research relevant to the eBLMP equation
  3. Motivation
  4. Framework
  5. Lie Symmetry Analysis of the Non-linear Extended BLMP Equation
  6. Building a one-dimensional optimal subalgebra system
  7. Commutator table
  8. Calculation of invariants
  9. Calculation of adjoint table and adjoint transformation matrix
  10. Optimal system of subalgebras in single dimension
  11. Symmetry groups of eBLMP equation
  12. Reductions of symmetry and new solutions
  13. Case 1:
  14. Case 2:
  15. Conservation Laws: Multiplier Approach
  16. ...and 2 more sections

Key Result

Theorem 2.1

The five-dimensional Lie algebra $L_5$ formed by the infinitesimal symmetries for the $(2+1)$-dimensional eBLMP system eq:1 is spanned by the following vector fields:

Figures (3)

  • Figure 1: Graphical analysis of solution in \ref{['eq:1A']}
  • Figure 2: Solution profiles for equations \ref{['eq:47a']}
  • Figure 3: Solution profiles of \ref{['eq:A']} and \ref{['eq:B']}

Theorems & Definitions (1)

  • Theorem 2.1