An energy-consistent dispersive shallow-water model

The flow of inviscid liquid in a shallow layer with free surface is revisit ed in the framework of the Boussinesq approximation. The unnecessary approx imations connected with the moving frame are removed and a Boussinesq model is derived which is Galilean invariant to the leading asymptotic order. Th e Hamiltonian structure of the new model is demonstrated. The conservation and/or balance laws for wave mass, energy and wave momentum (pseudo-momentu m) are derived. A new localized solution is obtained analytically and compa red to the classical Boussinesq sech. Numerical simulation of the collision of two solitary waves is conducted and the impact of Galilean invariance o n phase shift is discussed. (C) 2001 Elsevier Science B.V. All rights reser ved.