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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:
34A05Methods of solution of ODE
70H06Completely integrable systems and methods of integration (mechanics of particles and systems)
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References:
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