Conservation laws and invariant solutions of the wave equation on Bianchi I space–time: A comprehensive analysis

Optik ◽  
2021 ◽  
Vol 231 ◽  
pp. 166364
Author(s):  
Muhammad Alim Abdulwahhab
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Space Time ◽  
Comprehensive Analysis ◽  
Invariant Solutions ◽  
Bianchi I

Symmetries and generalized higher order conserved vectors of the wave equation on Bianchi I spacetime

2017 ◽  
Vol 14 (02) ◽  
pp. 1750028 ◽  
Author(s):  
Muhammad Alim Abdulwahhab ◽  
Adil Jhangeer
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Physical Process ◽  
Higher Order ◽  
Lie Symmetries ◽  
Invariant Solutions ◽  
Bianchi I ◽  
Exact Invariant

Conservation laws of various systems have been studied for decades due to their unparalleled importance in unraveling systems’ intricacies without having to go into microscopic details of the physical process involved. Their association with symmetries has not only had a stupendous impact in the formulation of the fundamental laws of physics, but also open doors to further explorations and unifications of others. In this study, we present the Lie symmetries and nonlinearly self-adjoint classifications of the wave equation on Bianchi I spacetime. For different forms of the metric potentials, generalized higher order non-trivial conserved vectors are constructed. Some exact invariant solutions are also exhibited.

Nonlinear self-adjointness and invariant solutions of a 2D Rossby wave equation

Open Physics ◽  
2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Rodica Cimpoiasu ◽  
Radu Constantinescu
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Lie Algebra ◽  
Rossby Wave ◽  
Invariant Solutions ◽  
Infinite Dimensional ◽  
Beta Plane ◽  
Variational Structure ◽  
Similarity Invariant ◽  
Linear And Nonlinear

AbstractThe paper investigates the nonlinear self-adjointness of the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane. It is a particular form of Rossby equation which does not possess variational structure and it is studied using a recently method developed by Ibragimov. The conservation laws associated with the infinite-dimensional symmetry Lie algebra models are constructed and analyzed. Based on this Lie algebra, some classes of similarity invariant solutions with nonconstant linear and nonlinear shears are obtained. It is also shown how one of the conservation laws generates a particular wave solution of this equation.

scholarly journals Wave Equations in Bianchi Space-Times

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
S. Jamal ◽  
A. H. Kara ◽  
R Narain
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Bianchi Type ◽  
Space Time ◽  
Noether Symmetry ◽  
Invariant Solutions ◽  
Type Iii ◽  
Symmetry Generators

We investigate the wave equation in Bianchi type III space-time. We construct a Lagrangian of the model, calculate and classify the Noether symmetry generators, and construct corresponding conserved forms. A reduction of the underlying equations is performed to obtain invariant solutions.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

A space-time BIE method for wave equation problems: the (two-dimensional) Neumann case

2013 ◽  
Vol 34 (1) ◽  
pp. 390-434 ◽  
Author(s):  
S. Falletta ◽  
G. Monegato ◽  
L. Scuderi
Keyword(s):  
Wave Equation ◽  
Space Time ◽  
Two Dimensional

Euler operators and conservation laws of the BBM equation

1979 ◽  
Vol 85 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Calculus Of Variations ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Formal Calculus ◽  
Euler Operators ◽  
Bbm Equation

AbstractThe BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

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