scholarly journals INTRINSIC FORMULATION OF GEOMETRIC INTEGRABILITY AND ASSOCIATED RICCATI SYSTEM GENERATING CONSERVATION LAWS

2009 ◽  
Vol 06 (05) ◽  
pp. 825-837 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Conservation Laws ◽  
Infinite Number ◽  
Integrability Theorem ◽  
Geometric Integrability

An intrinsic version of the integrability theorem for the classical Bäcklund theorem is presented. It is characterized by a one-form which can be put in the form of a Riccati system. It is shown how this system can be linearized. Based on this result, a procedure for generating an infinite number of conservation laws is given.

Notes on “infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system [Int. J. Mod. Phys. B 33 (2019) 1950147]

2021 ◽  
pp. 2150141
Author(s):  
Ning Zhang ◽  
Xi-Xiang Xu
Keyword(s):  
Conservation Laws ◽  
Darboux Transformation ◽  
Infinite Number ◽  
Lattice System ◽  
Darboux Transformations ◽  
Integrable Lattice

We show that the Darboux transformation in “Infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system” [Int. J. Mod. Phys. B 33 (2019) 1950147] is incorrect, and construct a correct Darboux transformation.

Symmetry Reduction, Exact Solutions, and Conservation Laws of the (2+1)-Dimensional Dispersive Long Wave Equations

2009 ◽  
Vol 64 (9-10) ◽  
pp. 597-603 ◽  
Author(s):  
Zhong Zhou Dong ◽  
Yong Chen
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Symmetry Group ◽  
Infinite Number ◽  
Wave Equations ◽  
Direct Method ◽  
Discrete Groups ◽  
Point Symmetry Group ◽  
Long Wave ◽  
Full Symmetry

By means of the generalized direct method, we investigate the (2+1)-dimensional dispersive long wave equations. A relationship is constructed between the new solutions and the old ones and we obtain the full symmetry group of the (2+1)-dimensional dispersive long wave equations, which includes the Lie point symmetry group S and the discrete groups D. Some new forms of solutions are obtained by selecting the form of the arbitrary functions, based on their relationship. We also find an infinite number of conservation laws of the (2+1)-dimensional dispersive long wave equations.

Die Struktur der Invarianzgruppe für lineare Feldtheorien

1966 ◽  
Vol 21 (11) ◽  
pp. 1826-1828 ◽  
Author(s):  
H. Steudel
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Lie Algebra ◽  
Infinite Number ◽  
General Property ◽  
Invariance Group

The LIE algebra U of the invariance group of any field theory with a homogeneous quadratic Lagrangian shows a remarkable structure: If D1, D2, D3 are any three elements of U then the expression ½ (D1 D2 D3 +D3 D2 D1) also belongs to U.This general property allows, starting with known invariance transformations or conservation laws, to derive an infinite number of conservation laws.

scholarly journals New asymptotic conservation laws for electromagnetism

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sayali Atul Bhatkar
Keyword(s):  
Electromagnetic Field ◽  
Conservation Laws ◽  
Infinite Number ◽  
Conservation Law ◽  
Classical Limit ◽  
Soft Photon ◽  
Memory Term ◽  
Late Time

Abstract We obtain the subleading tail to the memory term in the late time electromagnetic radiative field generated due to a generic scattering of charged bodies. We show that there exists a new asymptotic conservation law which is related to the subleading tail term. The corresponding charge is made of a mode of the asymptotic electromagnetic field that appears at $$ \mathcal{O} $$ O (e5) and we expect that it is uncorrected at higher orders. This hints that the subleading tail arises from classical limit of a 2-loop soft photon theorem. Building on the m = 1 [41, 42] and m = 2 cases, we propose that there exists a conservation law for every m such that the respective charge involves an $$ \mathcal{O} $$ O (e2m+1) mode and is conserved exactly. This would imply a hierarchy of an infinite number of m-loop soft theorems. We also predict the structure of mth order tails to the memory term that are tied to the classical limit of these soft theorems.

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