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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 5, issue 1
Nonlin. Processes Geophys., 5, 3–12, 1998
https://doi.org/10.5194/npg-5-3-1998
© Author(s) 1998. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
Nonlin. Processes Geophys., 5, 3–12, 1998
https://doi.org/10.5194/npg-5-3-1998
© Author(s) 1998. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Mar 1998

31 Mar 1998

Hamiltonian formulation for the description of interfacial solitary waves

R. Grimshaw1 and S. R. Pudjaprasetya2 R. Grimshaw and S. R. Pudjaprasetya
  • 1Department of Mathematics and Statistics, Monash University, Clayton, Victoria 3168, Australia
  • 2Department of Mathematics, Institut Teknologi, Bandung 40132, Indonesia

Abstract. We consider solitary waves propagating on the interface between two fluids, each of constant density, for the case when the upper fluid is bounded above by a rigid horizontal plane, but the lower fluid has a variable depth. It is well-known that in this situation, the solitary waves can be described by a variable-coefficient Korteweg-de Vries equation. Here we reconsider the derivation of this equation and present a formulation which preserves the Hamiltonian structure of the underlying system. The result is a new variable-coefficient Korteweg-de Vries equation, which conserves energy to a higher order than the more conventional well-known equation. The new equation is used to describe the transformation of an interfacial solitary wave which propagates into a region of decreasing depth.

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