Discovery of Conservation Laws via Matrix Search

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

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Noether’s invisible hand – A way of directly relating both nonlocal and local dynamical laws to associated conservation laws

Symmetry Culture and Science ◽

10.26830/symmetry_2018_4_487 ◽

2018 ◽

Vol 29 (4) ◽

pp. 487-505

Author(s):

Laurence I. Gould

Keyword(s):

Conservation Laws ◽

Invisible Hand

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An analogy between electromagnetic and internal waves

Доклады Академии наук ◽

10.31857/s0869-56524854428-433 ◽

2019 ◽

Vol 485 (4) ◽

pp. 428-433

Author(s):

V. G. Baydulov ◽

P. A. Lesovskiy

Keyword(s):

Angular Momentum ◽

Conservation Laws ◽

Internal Wave ◽

Special Relativity ◽

Internal Waves ◽

Maxwell Equations ◽

Wave Equations ◽

Lagrange Function ◽

Lorentz Transformations ◽

Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

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Large Time Step Godunov Method for 2-D Conservation Laws

Acta Analysis Functionalis Applicata ◽

10.3724/sp.j.1160.2010.00097 ◽

2010 ◽

Vol 12 (2) ◽

pp. 97-109

Author(s):

Hairui WEN ◽

Jinghua WANG

Keyword(s):

Conservation Laws ◽

Large Time ◽

Godunov Method ◽

Time Step ◽

Large Time Step

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