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Equadiff 82 pp 107–114Cite as

Some evolution equations arising in physics

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Water Wave
  • Burger Equation
  • Collisionless Plasma
  • Dissipative Medium
  • Generalize Burger

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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