Computation of conservation laws associated with the Maxwell equations by means of the quasi self adjoint method

Document Type : Research Article

Authors

1 Assistant Professor, Faculty of Mathematical Sciences, Shahrekord University

2 Associate Professor, Department of Physics, Shahrekord University

3 MSc student, Department of Physics, Shahrekord University

Abstract

In this paper and by applying the quasi self adjoint method, introduced by Ibragimov in 2011, we construct some conservation laws of the Maxwell equations in vacuum. Notice that since the number of equations is not equal to that of the unknowns in this system, one never finds any certain Lagrangian associated to it. Nevertheless, by omitting two equations, one receives a certain reduced system of differential equations having quasi self adjointness and appropriate to apply Ibragimov’s method for constructing its associated conservations laws without necessitating any Lagrangian. This subsequently gives as well some conservation laws of the Maxwell equations. It may be worth to notice that Ibragimov, himself, has computed some conservation laws of the Maxwell equations by means of the self adjoint method in 2009. Nevertheless, due to the fact that in contrary to the quasi self adjoint method, it is possible to construct the Lagrangian associated with the reduced system of equations, thus the approach of quasi self adjointness employed in this paper includes some partly different complexities.

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