Abstract:
Nonlinear dispersive shallow water equations on a sphere are obtained without using the potential flow assumption. Boussinesq-type equations for weakly nonlinear waves over a moving bottom are derived. It is found that the total energy balance holds for all obtained nonlinear dispersive equations on a sphere.
Keywords:shallow water equations on a sphere, surface waves, nonlinear dispersive equations, Boussinesq type equations, energy conservation law.
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