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There are many similarities between electromagnetic waves and sound waves. Maxwell’s equation is the oldest gauge theory. Three main aspects of gauge theory are considered: (1) symmetries, (2) gauge invariance, (3) covariant form of the wave equation. Two of my discoveries mentioned in my earlier papers are revisited here: (1) symmetries of velocity field and stress field in the acoustic equations...
The evolution equations of Maxwell’s equations has a Lagrangian written in terms of the electric E and magnetic H fields, but admit neither Lorentz nor conformal transformations. The additional equations ∇⋅E=0, ∇⋅H=0 guarantee the Lorentz and conformal invariance, but the resulting system is overdetermined, and hence does not have a Lagrangian. The aim of the present paper is to attain a harmony...
We generate conservation laws for the Burridge–Knopoff equation which model nonlinear dynamics of earthquake faults by a new conservation theorem proposed recently by Ibragimov. One can employ this new general theorem for every differential equation (or systems) and derive new local and nonlocal conservation laws. Nonlocal conservation laws comprise nonlocal variables defined by the adjoint equations...
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