Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 318, Issue 2, Pages 742-757Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2005.11.012
Keywords
integrating factor for higher-order equations; adjoint equation to non-linear equations; Lagrangian; Noether's theorem
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Integrating factors and adjoint equations are determined for linear and non-linear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables. The method is illustrated by considering several equations traditionally regarded as equations without Lagrangians. Noether's theorem is applied to the Maxwell equations. (c) 2005 Elsevier Inc. All rights reserved.
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