55 research outputs found
Nonlinear self-adjointness in constructing conservation laws
The general concept of nonlinear self-adjointness of differential equations
is introduced. It includes the linear self-adjointness as a particular case.
Moreover, it embraces the previous notions of self-adjoint and quasi
self-adjoint nonlinear equations. The class of nonlinearly self-adjoint
equations includes, in particular, all linear equations. Conservation laws
associated with symmetries can be constructed for all nonlinearly self-adjoint
differential equations and systems. The number of equations in systems can be
different from the number of dependent variables
Conservation laws for the Maxwell-Dirac equations with a dual Ohm's law
Using a general theorem on conservation laws for arbitrary differential
equations proved by Ibragimov, we have derived conservation laws for Dirac's
symmetrized Maxwell-Lorentz equations under the assumption that both the
electric and magnetic charges obey linear conductivity laws (dual Ohm's law).
We find that this linear system allows for conservation laws which are
non-local in time
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