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 Lie algebra classification, conservation laws and invariant solutions for modification of the generalization of the Emden--Fowler equation.

2021 ◽  
Author(s):  
Yeisson Acevedo Agudelo ◽  
Gabriel Loaiza Ossa ◽  
Oscar Londoño Duque ◽  
Danilo García Hernández
Keyword(s):  
Conservation Laws ◽  
Lie Algebra ◽  
Invariant Solutions ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Generating Operators ◽  
Variational Symmetries ◽  
The Given ◽  
Lie Algebra Classification ◽  
Fowler Equation

We obtain the optimal system’s generating operators associated to a modification of the generalization of the Emden–Fowler Equation. equation. Using those operators we characterize all invariant solutions associated to a generalized. Moreover, we present the variational symmetries and the corresponding conservation laws, using Noether’s theorem and Ibragimov’s method. Finally, we classify the Lie algebra associated to the given equation.

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.

Group classification and conservation laws of the generalized Klein–Gordon–Fock equation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640023
Author(s):  
B. Muatjetjeja
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Algebra ◽  
Group Classification ◽  
Noether Symmetries ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Klein Gordon

In the present paper, we perform Lie and Noether symmetries of the generalized Klein–Gordon–Fock equation. It is shown that the principal Lie algebra, which is one-dimensional, has several possible extensions. It is further shown that several cases arise for which Noether symmetries exist. Exact solutions for some cases are also obtained from the invariant solutions of the investigated equation.

scholarly journals Polynomial ring representations of endomorphisms of exterior powers

2021 ◽  
Author(s):  
Ommolbanin Behzad ◽  
André Contiero ◽  
Letterio Gatto ◽  
Renato Vidal Martins
Keyword(s):  
Lie Algebra ◽  
Polynomial Ring ◽  
Vertex Operators ◽  
Exterior Power ◽  
Infinite Dimensional ◽  
Symmetric Structure ◽  
Rational Polynomials ◽  
Exterior Powers ◽  
Vertex Representation ◽  
Countably Infinite

AbstractAn explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document