Modeling Energy Conservation in a Completely Integrable Boussinesq system

Ali A., Kalisch H.

This work presents a derivation of the energy density and energy flux of water waves modeled by the so-called Kaup system, a variant of the Boussinesq system. The derivation is based on reconstruction of the velocity field and the pressure in the fluid column below the free surface, and is an extension of a method recently proposed by the authors. In the present note, it is shown that the total energy of the wave system is equal to the Hamiltonian function found by Craig and Groves.

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