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Integrating factors, adjoint equations and Lagrangians. (English) Zbl 1102.34002
A new concept of an adjoint equation is used for construction of a Lagrangian for any system of differential equations. The method presented is illustrated by considering several equations traditionally regarded as equations without Lagrangians. Noether’s theorem is applied to the Maxwell equations.

MSC:
34A05 Explicit solutions, first integrals of ordinary differential equations
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
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