Boussinesq approximation for water waves

Summary

The Boussinesq approximation for water waves is a family of model equations for long water waves of small amplitude in shallow water. It keeps the leading effects of both nonlinearity and dispersion, assumed to be of the same small order, and drops the vertical coordinate. The result is a system of equations in the horizontal variables only, which is far cheaper to solve than the full free boundary problem. It contains the shallow water equations as its non-dispersive limit and leads to the Korteweg–de Vries equation for waves moving in one direction.