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Application of the similarity method to the nonlinear Boltzmann equation

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Abstract

A consequent application of the similarity method to the nonlinear Boltzmann equation leads to the general form of exact similarity solutions and allows a group-theoretic classification. Classes of similarity solutions depending very strongly on the source term but different from the Bobylev-Krook-Wu solution will be discovered and discussed.

Zusammenfassung

Eine konsequente Anwendung der Similarity-Methode auf die nichtlineare Boltzmanngleichung führt auf die allgemeine Form der exakten Lösungsstruktur und erlaubt eine strenge Klassifikation der Similarity-Lösungen. Neben der Bobylev-Krook-Wu Lösung werden weitere Lösungsklassen gefunden und diskutiert, die sehr stark von der Wahl des Quellterms abhängen.

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Author notes

  1. Theo F. Nonnenmacher

    Present address: Dept. for Mathematical Physics, University of Ulm, D-7900, Ulm, Germany

Authors and Affiliations

  1. Center for Studies of Nonlinear Dynamics, La Jolla Institute, La Jolla, Ca, USA

    Theo F. Nonnenmacher

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  1. Theo F. Nonnenmacher
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Nonnenmacher, T.F. Application of the similarity method to the nonlinear Boltzmann equation. Z. angew. Math. Phys. 35, 680–691 (1984). https://doi.org/10.1007/BF00952113

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  • DOI: https://doi.org/10.1007/BF00952113

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