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Some evolution equations arising in physics

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Equadiff 82

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1017))

Abstract

In this paper we consider a new series of evolution equations generalizing the Korteweg-deVries (KdV) and Burgers equations, and we report recent advances on these equations together with the physical phenomena where they arise. In particular we consider a generalized Burgers' equation and we sketch a method for solution in series by using the theory of Sobolevskij and Tanabe. Then we study the KdV equation with nonuniformity terms and we describe various physical interpretation of this equation. We consider various particular cases in which varying solitonic solutions exist. Also we sketch a unicity theorem. Finally modified Burgers-KdV equations are considered.

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Author information

Authors and Affiliations

  1. Istituto Matematico, Facoltà di Ingegneria-Università di Palermo, Italy

    T. Brugarino

  2. Dipartimento di Matematica, Università della Calabria-Cosenza, Italy

    A. Canino & P. Pantano

Authors
  1. T. Brugarino
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  2. A. Canino
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  3. P. Pantano
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Editor information

H. W. Knobloch Klaus Schmitt

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© 1983 Springer-Verlag

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Brugarino, T., Canino, A., Pantano, P. (1983). Some evolution equations arising in physics. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103241

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  • DOI: https://doi.org/10.1007/BFb0103241

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12686-7

  • Online ISBN: 978-3-540-38678-0

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