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Conservation laws—a simple application to the telegraph equation

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Abstract

Conservation laws are a recognized tool in physical and engineering sciences. The classical procedure to construct conservation laws makes use of Noether’s Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be determined. A broader class of such laws is obtained, if Noether’s Theorem is applied together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. The same conservation laws can be obtained by using the Neutral-Action method with the advantage that only one set of unknown functions is required. Moreover, the Neutral-Action method is also applicable in the absence of a Lagrangian, since for this procedure only the governing differential equations are needed. By this, the Neutral-Action method appears to be the most useful tool in constructing conservation laws for systems with dissipation.

The intention of this paper is to give a reference for further research on this topic rather than showing some detailed calculation on a special subject. Thus, the Neutral-Action method is introduced in detail and is applied to a simple example (the telegraph equation) to show the usefulness of this procedure for further applications in electronics.

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Authors and Affiliations

  1. Department of Production Engineering, University of Bremen, IW3-FB4, PO Box 330 440, 28334, Bremen, Germany

    Uwe Nordbrock & Reinhold Kienzler

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  1. Uwe Nordbrock
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  2. Reinhold Kienzler
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Correspondence to Uwe Nordbrock.

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Nordbrock, U., Kienzler, R. Conservation laws—a simple application to the telegraph equation. J Comput Electron 7, 47–51 (2008). https://doi.org/10.1007/s10825-008-0250-2

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  • DOI: https://doi.org/10.1007/s10825-008-0250-2

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