Summary
A modification of Bergman's integral operator method is applied to a hodograph system descriptive of linearly polarised plane electromagnetic pulse propagation in non-linear dielectrics. Series solutions of the system are thereby generated corresponding to general D-E and B-H relations. For certain non-linear ‘constitutive laws’ the governing wave propagation equations are reduced to a hyperbolic canonical form associated with the classical wave equation and closed form integration is thereby achieved. The availability of arbitrary parameters in these laws allows approximation to non-linear dielectric laws derived empirically. Moreover, it is noted how a generalised version of Weinstein's Correspondence Principle may be utilised to generate iteratively more general non-linear constitutive laws for which reduction to canonical form may be obtained.
Zusammenfassung
Eine Modifikation der Bergmanschen Integraloperatorenmethode wird auf ein, die Ausbreitung linear-polarisierter ebener elektromagnetischer Wellen in einem nichtlinearen Dielektrikum beschreibendes Hodographensystem angewendet. Allgemeinen D-E- und B-H-Beziehungen entsprechende Lösungen des Systems in Form von Reihen werden dadurch hergeleitet. Für bestimmte nichtlineare Werkstoffgesetze reduzieren sich die Grundgleichungen der Wellenausbreitung zu einer hyperbolischen kanonischen Form (der klassischen Wellengleichung) und ermöglichen eine geschlossene Lösung. In diesen Gesetzen auftretende freie Parameter gestatten die Anpassung an empirisch ermittelte nichtlineare Werkstoffgesetze. Weiter wird gezeigt, wie eine Verallgemeinerung des Weinsteinschen Korrespondenzprinzips zur iterativen Erzeugung allgemeiner nichtlinearer Werkstoffgesetze, für die Reduktionen auf kanonische Formen möglich sind, verwendet werden kann.
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Rogers, C., Cekirge, H.M. & Askar, A. Electromagnetic wave propagation in non-linear dielectric media. Acta Mechanica 26, 59–73 (1977). https://doi.org/10.1007/BF01177136
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DOI: https://doi.org/10.1007/BF01177136