Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 5 1 1998 10.5194/npg-5-3-1998 http://www.nonlin-processes-geophys.net/5/3/1998/ http://www.nonlin-processes-geophys.net/5/3/1998/npg-5-3-1998.html http://www.nonlin-processes-geophys.net/5/3/1998/npg-5-3-1998.pdf 3 12 0000-00-00 Hamiltonian formulation for the description of interfacial solitary waves R. Grimshaw S. R. Pudjaprasetya Department of Mathematics and Statistics, Monash University, Clayton, Victoria 3168, Australia Department of Mathematics, Institut Teknologi, Bandung 40132, Indonesia 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.