Phase modulated solitary waves controlled by bottom boundary condition
  A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced kdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition whereas amplitude remains constant. 
Abhik Mukherjee and M.S. Janaki
nlin.PS physics.flu-dyn